Firstly, see My question is about forks in general. If I have a portion of a coin do I get the exact portion of that new coin? regarding the duplication of tokens in a fork. Secondly, it depends on the token. In general, for utility tokens and tokens that act like securities, the issuer of the token will only respect tokens from one of the forks. For example, Storj.io allows people to store data in their crowd-sourced cloud for STORJ tokens (tokens on the main Ethereum chain). If there were to be a fork of the main chain, they would likely have a node that monitors transactions on only one of the two forks -- the tokens on the other are useless. Similarly, if a company were to record share transfers on the blockchain, it would likely ignore transactions on one of the forked chains. In reality, you cannot fork a company's non-digital assets (nor digital monetary assets), so the tokens on whichever fork the company chooses to honour after the split is the one(s) that matter.
There is nothing legally preventing the company from honouring both, but the sum of the owner's equity must still be 100%. For example, company XYZ has $100 worth of assets and 100 tokens on the main net. Each share entitles the owner to $1 if the company were liquidated. Now, suppose a fork happens that leaves people with 100 XYZ tokens on Ethereum and Ethereum-NewClassic. If XYZ is liquidated, it has $100 to distribute. It cannot give $1 per Ethereum-XYZ token AND $1 per Ethereum-NewClassic-XYZ token since it only has $100 in real-world assets.
Less obviously, in the STORJ example, if a user is entitled to 1 GB per month per STORJ token and a fork happens, STORJ would (potentially) not be able to honour 1 GB per month per STORJ token on both chains (again, it's an asset division problem)
A real example of a forked token was TheDAO; on one of the chains, the tokens were honoured as written (Ethereum Classic). But, given the bug (according to most people) in the contract, the Dao was greatly drained by the Dao attacker and the tokens had far less value in terms of ETC than what was taken as par moments before the attack. Meanwhile, on the main net, a Dao token is worth around 0.01 ETH since that is what can be withdrawn for each Dao token.
Another real example is the Tether token which (supposedly) is backed by US dollars. When Bitcoin forked, I believe this also meant all Omni tokens, of which Tether is one, also forked. However, Tether obviously did not suddenly have twice as many US dollars as a result. Thus, it would have to pick and choose a chain for which to honour tokens.
P.S. Ethereum Gold is a thing.