There are more exchanges than listed here, I have just thrown together some popular ones as well as a link to a background on each.
circle.com My Favorite place to purchase Bitcoin.
Bitsource.org (based in Belize)
coinsimple.com Easily accept Bitcoin Payments… great for Businesses
coinport.com CryptoCurrency Exchange
bitcoinx.io List of hundreds of exchanges with ratings
Like I said there are more than listed here, these are the most popular ones. However, if you would like to see a complete list of all exchanges click here.