Coinbase / GDAX
Coinbase is a San Francisco based corporation that was founded by Brian Armstrong and Fred Ehrsam in June of 2012. Since its inception Coinbase has created its eponymous Bitcoin wallet service with ACH transfers, and an order book based exchange called GDAX.
Although Coinbase bills itself as a wallet, it should not be used to store Bitcoin, only to buy and sell Bitcoin for fiat. Coinbase serves as a custodial wallet, meaning that it is not a secure, trust-less Bitcoin wallet and storing coins there is not advisable due to serious security and privacy problems. Coinbase also monitors all activity on accounts, so it is advised that no notes be left on any transactions and users should only send transactions to themselves, not to any third parties.
Coinbase offers an easy way to buy Bitcoin based on a trust mechanism: when trading coins using a slow and reversible method like ACH, Coinbase takes a risk, assumes the transfer will complete and locks in a price for the coins based on the present price. Coinbase also offers credit and debit card exchanges at an increased fee.
Coinbase's Wallet service also offers a way to act as a proxy to send funds to an email address, a way to send invoices, and a payment processing service.
Coinbase launched an order book based exchange marketplace in January of 2015. The exchange integrates with their wallet's banking integrations, but offers a widely different fee structure. To encourage standing orders and exchange liquidity, the exchange waves its fee for makers, trades made against standing orders.