MtGox requires a fair bit of verification, but they've also been around pretty much the longest, and have already had to deal with all the security issues that other bitcoin sites are only beginning to discover. I trust them.
(That is to say, I trust them long enough to do the exchange, and then I transfer the bitcoins to my private offline wallet as soon as possible. And you should too.)
(That is to say, I trust them long enough to do the exchange, and then I transfer the bitcoins to my private offline wallet as soon as possible. And you should too.)