Is there any way I can use a blockchain explorer or similar tool to find out how much activity there is on addresses for specific ethereum based services (Digix, Augur etc. pp.)?
Yes you can if you know the address. Just use any of the blockexplorers such as :
Etherscan.io, Etherchain.org or Live.ether.camp. You can see past transactions and the internal contract invocations. This gives you a good indication of "activity".
For more information on block explorers see What Ethereum blockchain explorers exist?
Using blockchain explorers for quickly checking transaction or a specific smart contract activity is ok. But it gets tricky when you want to do real monitoring on the long run as :
1 - you don't have any control on what is scanned or what information
2 - the service is not local, so you are at risk any moment the service is not available
3 - Since these explorers take the task of monitoring and reporting activity about the whole blockchain you will end up with some restrictions etherscan, for the example doesn't process requests that return more than 10,000 transactions.
The solution is to create a local tool that you can run on your system or server that will monitor specific addresses you specify and return the whole activity they conduct.
Checkout https://github.com/Neufund/smart-contract-watch it's open source so you can anything you want with it.
You can use a number of blockchain explorers to see the transactions coming to/from a given Ethereum address.
To do this through EthTools.com you can simply enter the address in the search bar displayed on the right hand side of the header.
This will take you to a screen similar to the below from which you can deep dive into the details of specific transactions.
Disclaimer: My company built EthTools.com
At QuickBlocks, we're building a fully client-side decentralize explorer. All the solutions mentioned above are centralized, and there, in our opinion, less applicable.