AirSwap is working to create a decentralized peer-to-peer exchange for ERC-20 tokens. Instead of using a centralized order book to execute trades, AirSwap is developing an indexer that will act like a search engine to connect traders. The AirSwap Oracle gives pricing recommendations in a way that is drastically different than the market maker pricing of centralized exchanges. The exchange is fueled by the AST token, which allows anyone to become a liquidity maker.

BitFinex is a bitcoin to fiat exchange, a margin trading exchange, and a liquidity provider. The platform offers a number of features that expand the financial positions you can take - for example the ability to short Bitcoin via margin trading.
The exchange also offers a set of other cryptos apart from bitcoin such as Litecoin and Ethereum.
Deposits and withdrawals take place via the standard bank transfer means with fees of 0.1% and a minimum of $20. Bitcoin and Litecoin are free.
BitFinex takes security seriously and have moved from a hot wallet cold wallet set up to segregating customer funds where each user has access to their own wallet which they can review on the blockchain.
Bitfinex was hacked on 03 August 2016 and around 120,000 BTC were stolen.
Fee of 0.1% for most trades