Cobinhood is a cryptocurrency exchange with no trading fees. Users can trade most of the major pairs, and a variety of other currencies. Cobinhood offers both both a centralized and a decentralized trading platform. In addition to their cryptocurrency exchange, Cobinhood also operates an ICO underwriting service, and they are releasing Zeux, which will be a crypto mobile payment and investment app.
The network is powered by the COB token.

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

Kraken is a US-based cryptocurrency exchange and one of the largest bitcoin exchanges in terms of volume and liquidity.
It provides Bitcoin pricing to the Bloomberg Terminal and has considerable influence on the overall crypto market. Kraken offers a number fiat funding and transfer options.
There are 18 BTC pairs and 16 USD pair to trade
Fees vary depending on the volume - for main trading pairs this is between 0.1-0.35% - however for other less common crypto pairs the range can be as low as 0.05% or as high as 0.75%. There are also 0% fees for some trades.
Withdrawals and deposits are variable depending on the method - although in general all fees are 0.19% with a $20 minimum.