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

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.

Bittrex is one of the largest crypto to crypto exchanges. It offers a large number of trading pairs, but do not allow fiat to crypto trading. Bittrex has one of the largest trading volumes in the market.
It is a reputable exchange with good record on security and is also fully regulated. They provide two factor authentication as well as a number of other options to secure funds. They are United States based and are fully compliant with all laws.
They support more than 190 cryptocurrencies and have a dynamic platform. It’s a good option for both advanced and beginner traders; providing advanced tools like candlestick charts and crosshairs, but with a user-friendly interface that is very intuitive.
Trading Fees: 0.25%