One of the more popular exchanges right now is Mt.gox, but they only have Bitcoin available for trading. My personal preference is to use BTC-E. There are many more currencies available like Bitcoin, Litecoin, Feathercoin, Chinacoin, Novacoin, and Terracoin.  The site is secure and has a ongoing chat room for questions. The charts are also helpful for people who want to day trade. There is also a very handy BTC-E app for Android folks (the widgets are great if you’re not home). Now there are probably many more exchanges but these are the 2 main ones I would trust.

Links:

Mt.Gox: https://mtgox.com/

BTC-E: https://btc-e.com/