BCEX is a top 20 exchange that is aimed at the Chinese crypto market.

Trading Fee: 0%-0.2%
Withdrawal Fee: 0%-0.5%
Number of Tokens/Coins: 51

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

Poloniex is an established crypto to crypto exchange that is based in the United States. It offers a large selection of tokens to trade and has high liquidity. Poloniex was hacked in 2014, and lost more than 12% of their bitcoin supply. They have improved their security protocols since then. In February, 2018 Poloniex was acquired by Circle, one of the largest crypto payment providers.

Trading Fee: 0%-0.1% Maker and 0%-0.2% Taker
Deposit Fee: Varying Depending on blockchain fees
Withdrawal Fee: Varying Depending on blockchain fees
Number of Tokens/Coins: 97