Coinbase is the biggest Bitcoin broker / exchange around, supporting 32 countries and with more than 4 million customers around the world.
Founded in 2012 as part of Ycombinator Coinbase is also one of the oldest exchanges around. Coinbase is a regulated and licensed company.
Coinbase allows users to buy and sell Bitcoins through their bank account, credit card, Paypal account (selling only), and other less known methods as well. Even though Coinbase has started out only as a broker (selling Bitcoins directly to customers), lately (May 2016) Coinbase started operating GDAX – A Bitcoin exchange, where Bitcoiners can trade Bitcoins with one another.
Lowest fees in the market
Screenshots from website