Howdy,
I've been using one for a couple months now and it's given no reason to mistrust it. But it seems weird to me sending my money to an intermediary that's neither a wallet nor a bank and is entirely online. Feels like the money is hanging out in some nowhere zone that isn't completely under my control...
Dies any one else feel this way or do I just not understand this stuff well enough yet?
Thanks!
It's definitely a shot in the dark if you aren't dealing with a reputable/responsible and well funded exchange. For instance, it is known that Coinbase is pretty much the most capitalized company in the space aside from 21, and it can be expected that their security practices would be par-none. For the most part, it's tough to know how secure the other large exchanges are.
As good practice, it's probably best not to keep your coins sitting on any exchange for a long time.
Mt gox was pretty trusted among many people too. Since coinbase only operates in US and there are some people who aren't from US, it isn't a good choice. Your best choice is to choose an exchange which has a proof of solvency audit available for you to review. It should however only be used for references and shouldn't make the exchange automatically trusted. Audits can be unreliable as time passes though.