Most of the main exchanges have released documentation on how they're going to handle the switch. It's looking more and more like nothing exciting will happen, which is a relief to all investors. But who knows???
Supposedly a small number of miners will stick with "Bitcoin Classic" on August 1st, but most will go with SegWit2x. I think most exchanges plan to service only the SegWit2x branch. At least that's what Coinbase is going to do. This means that you will lose all coins on any other branch that may (or may not) split off.
IF THERE IS A SPLIT: If you have a lot of BTC at an exchange, it might be a good thing to send them to a wallet you control. That way, after the split you will eventually have access to both coins. You might have to wait until new wallet software is made, but as long as you have your private keys, they will work on both chains.