I think this question is out of scope for this stackexchange and voted to close it, but since it's still open... (note that the first several sections are greatly-simplified world-views and thus opinions; the last section is very subjective). N.B. that I do not possess a finance background and that for answering your question about intrinsic value, I'm using a definition aligned with an intrinsic theory of value, not a subjective one, as, say, working from a marginalistic framework; the rest is generally applicable.
Where does value come from?
Supply and demand
Things have value if there is a demand for them. The value is higher the harder it is to obtain them. For example, your family heirloom watch is one of a kind (due to its provenance) and may be priceless to you. However, the watch might be one of many to a watch collector and thus is of lower value. If the price a buyer is willing to pay for something is greater than the price the owner is willing to part with it for, then an exchange can take place. So if your watch would fetch $1000 on the open market, even if someone is willing to offer you $10000 for it, you wouldn't sell. Similarly, if you had a second watch that was otherwise identical to your heirloom watch, you'd accept an offer of $10000 but reject a low-ball offer of $900 since you could go elsewhere to sell it. Your classic supply and demand. Note that the intrinsic value of any two similar watches is equal: it is whatever the value of being able to keep time is (multiplied by the lifetime of the watches). The additional sentimental value of the heirloom is extrinsic (or subjective) value.
Let's look at fiat currencies, first. Why are they valuable? To understand that, we need to step back and look at asset-backed currencies. In the past (and now, but just to a different extent), people valued gold, beads, salt, livestock, furniture, etc. So someone who specialized in making furniture could create something of value (out of a lower-valued thing like raw wood) and could use it to obtain something s/he valued but didn't have much of, like food. In years of good harvests, the value of a chair might rise relative to the price of food; in times of famine, the opposite would likely happen; this effect would be particularly strong because people need food to survive (inelastic demand) but can do without chairs (elastic demand). The exchange of goods and service for other goods and services is, of course, the basis for bartering. However, governments, in order to function, consume resources (which are of value) such as materials and time. To obtain the resources, they would tax the fruits of labour and/or wealth and potentially exchange them for other things of value that they actually wanted. For example, being taxed in bushels of wheat and exchanging them for less-perishable gold. As we know, bartering can be burdensome (what if you want a cow and all I have is wheat? And let's not talk about transportation...) So IOUs or similar instruments came about: the gold-backed US currency was essentially an IOU for gold. But taxation must go on! So instead of getting paid in wheat, governments would dictate that they be paid in a currency that (usually) they printed. Thus, they are/were able to tax all forms of production, including widgets they had no direct interest in, and get paid in a more convenient manner.
Of course, in this scheme, when governments can threaten you with jail for not paying taxes and can make you pay them in the currency of their choice, there is no longer any need for this currency to even be tied to a finite resource. The government is limited in taxing people only by the number of people they can punish for not paying taxes. And, now, since every person (including companies, which are legally persons) is taxed (though not all are required to pay any tax, esp. low income individuals), regardless of how they acquire wealth, if an individual wishes to become wealthy, the price of admission is paying in (usually) fiat currency. Because there is a demand for fiat currency and is related to amount of wealth produced by an economy, you can now see why people say that fiat currencies are "backed by the economy". It's because we trust that people will continue to want to obtain wealth and, in order to do so, must produce/acquire other things of value and, in doing so, pay taxes. If I, as a yak merchant, wish to buy a bigger house, I must buy and sell more yaks and pay more taxes. So, in a way, it is greed and the threat of incarceration that give fiat currencies their value. Note that any particular fiat currency itself has little or no intrinsic value, but has extrinsic value because we assigned it a value. The idea of fiat currency does have intrinsic value, though, because of the benefits it affords. Thus, there is intrinsic value from adopting fiat currencies.
Whence does cryptocurrency derive value?
So... back to cryptocurrencies. As far as I know, no one is required to pay their taxes in cryptocurrencies, though in most cases they need to pay taxes on their cryptocurrencies. So does cryptocurrency have any value at all? It's a bunch of numbers that can be divorced from the real world, just as fiat currency can, so it has no intrinsic value.
However, Bitcoins (the currency) itself provides a service, which is of value: they allow transactions through the Bitcoin network. The Bitcoin network provides this value through the ability to relatively quickly send tokens (bitcoins, the currency) across the Internet according to a set of rules that have some economically useful properties: they are finite (limited supply), can be (theoretically) infinitely divided, easily and quickly transported, do not spoil, can be protected without a small army, ... and all on a public blockchain that can be interacted with by anyone with devices like smartphones and computers. The service is the Bitcoin network itself. Much of the value of Bitcoin is probably tied to speculation: as adoption of Bitcoin (the network) increases, the fees (cf. taxes) paid are still present and people are paying to use this transmission service that other people are using. It's like if you had to pay for using Twitter: other people are using Twitter exclusively and if you want to reach them and had to pay, you might pay some small (or large) amount. Because Bitcoin is the incumbent and has many users and is, perhaps, the best known, you get the most utility from reaching people over the Bitcoin network.
Ethereum, on the other hand, is a superset of the things Bitcoin is. In addition to being a value store as Bitcoin is (even if it wasn't intended as such, just like how yaks are not considered value stores but do store some value), Ethereum provides the ability to run programs that transfer its own tokens, ether, between accounts, and/or store data; this last aspect is used for things like ERC20 tokens and the now-defunct DAO.
Because these programs consume computational and storage resources, Ethereum incentivizes people to do the compute/storage work for the network. This is presently done through the process known as mining. The form of compensation is ethers, the native token of Ethereum. These computations and storage take are recorded in discrete units of work which we call "blocks". Miners are rewarded for empty blocks (the network needs to keep running, even if no transactions take place at any given moment) by the Ethereum protocol itself (i.e., the developers of Ethereum wrote some code that all users of Ethereum implicitly agree is fair or at least tolerable) and by users of Ethereum that perform transactions; the latter is the transaction fee.
Because ethers are a finite resource (it can grow infinitely, at present, but the actual supply is finite), this satisfies the "finite-supply/availability" criterion for something to have value. People who wish to transact on the Ethereum network must pay to use the network and the price for this is paid in ethers. The more people that use Ethereum, the more gas that will be consumed and the more total transaction fees will likely rise since this demand for ethers can only be met by participants in the initial crowdsale, founding members of the Ethereum Foundation, miners, and people who have received ethers. This scarcity creates value.
At present, empty blocks serve multiple purposes. These include "time keeping" on the blockchain and the regulation of difficulty. The difficulty maintenance is important to prevent fracturing of the network due to the latency-to-blocktime ratio; if this ratio is too high, then a fork, AKA chain-split, occurs. This is a bad situation and there is value to people submitting transactions to the blockchain to avoid this. Hence, it makes sense to allow these empty blocks, even if it means paying fees to the miners (in this case, it's a flat tax on capital; inflation in the network means existing holdings are worth fractionally less). In addition to marking the passage of time, they also periodically increase the total expended difficulty to maintain network synchronization and increase the cost of performing a 51% attack on existing transactions. A longer chain is a stronger chain.
My opinion about mining profits and cryptocurrency prices
Avoiding realizing loss
There is, I believe, a common misconception that the price of electricity dictates a floor for the price of ethers and bitcoin. Let us exclude crowdsale participants and Ethereum Foundation members for a moment. Let's also revisit the heirloom watch example. Just like people are averse to selling shares at a loss, many miners don't want to sell ethers at less than the price they paid to obtain them (in this case, via mining). If you never sell the watch, its price never gets discovered and the price for the average watch of that type is dictated by the price other people are willing to sell at.
In some cases, like for shareholders of Apple in the '90s, this holding pays off. In other cases, like for shareholders of Enron, this does not. Thus, if no one is selling their ethers unless they're at least breaking even, then the price of an ether is capped at the lowest price they paid to obtain them. In that situation, electricity might be a decent proxy. But there is nothing economically preventing someone from dumping a load of ethers onto the market, depressing prices below the price to mine (see the Ethereum flash crash).
Let's look at non-cryptocurrencies for a minute. Let's pretend you make coffins for a living (!). It costs $100 in materials for the coffin and you can make and sell one for $1000 every hour. Let's ignore the fact that people will switch jobs and compete with you at those rates. You are still not guaranteed to be able to sell the coffin for more than your expenses. Suppose cremation becomes in vogue or someone cures death. The need for coffins will drop and the coffins will be worth less than the wood they're made from. This is essentially what happened to the first several Zimbabwean dollars. And this is how companies go out of business. Just because you purchased inventory or services at a particular price does not mean someone will be willing to pay more for the product you produced as a result. For example, the hair-doll I made from vbuterin's hair trimmings cost me about $1000 to make (the price of twine, an elastic band, and gas + bribes to get hair from various barbershops in Toronto). That does not mean anyone would even pay a single cent for it.
Back to mining. If mining becomes unprofitable, we expect people who are mining purely for profit to stop mining unless they are expecting the price to rise again. The Ethereum network self-balances and makes it easier for remaining miners to find blocks/get rewarded ethers. But there is a time-value tradeoff for mining: people who are mining are tying up resources to mine which they could be applying to other enterprises, so even break-even miners might drop out. On the other hand, I think there are a lot of miners, especially recently, who are (pardon my generalization) unsophisticated investors/speculators and think of Ethereum as way to get-rich-quick. But, as with any other form of generating wealth, at some point, the benefits from mining outweigh whatever means of wealth generation other people were engaging in and people will become miners. This leads to a decreased share in the surplus (profits due to mining) from the overall market per miner, reducing their profitability and, ultimately, I believe the market will reduce the profitability to levels similar to investments of similar risk profiles (and, similarly, raise their profitability because fewer investors are in that space because they switched to mining).
Is it a bubble?
It is my belief that ICOs are currently a bubble: there is no current nor foreseeable situation for many of them to justify the valuation placed on them. My opinions about Bitcoin and Ethereum are less clear. The prices are high relative to the amount of utility I see them as actually providing. However, I believe that the price/earnings ratio of a stock or other investment is an overly-simplistic metric for measuring its value relative to other investments. I believe that price/earnings/growth is a better measure of value since it factors in the ability of an investment to generate future revenue. Unless you're buying a stock or other instrument below book value, when you buy it, you're buying future profits.
I think there is tremendous potential of utility for a highly interoperable medium of exchange such as Ethereum. Right now, the exchange of currency for stocks, foreign currencies, and other instruments usually requires trusted brokers. Even day-to-day transactions such as payment via credit card involves a chain of trust. But if these brokers can be turned into code -- where shareholders agreements are code while revenue and expenses operate on the same protocol which allows easy profit distribution (the distal reason people own share in a company) -- then that makes a more friction-free environment for exchanging goods and services.
The Euro zone is an example of unifying different "tokens". The Italian lira, the Greek drachma, and the French franc gave way to a single currency for exchange across the Euro zone. Some companies still deliberately create their own tokens so that they have more control over them (gift cards are an example of this), but Ethereum can reduce the difficulty and cost of setting up and maintaining such tokens. So even if it's a benefit to a company to transact with its customers mostly in Acme tokens, it can also be easier for end-users to use the tokens when they're in a single blockchain.
The higher the price of a stock, the less room for growth there is -- and the riskier the investment and the lower the returns. Similarly, the higher the price of ether, the riskier it is, from a profit-making standpoint, and the lower the final returns. So while the price of ether might be higher than the utility it currently provides, it's not obvious to me that the price paid today is entirely speculative: the value investor may have done the math and said that, if in 5 years, the price of an ether is (I'm not making a prediction... just throwing out a number to do easy math with) is $1000, the returns are about 38% per annum, compounded annually. That's not as good as if the price were $100 right now -- that would lead to a return of 60% PA, but still an amazing return. So there's less upside with the price being higher, but if they see future value, that's what they're buying into now, before that value is seen by others/is realized by the market.