Bitstamp is one of the most popular fiat to Bitcoin exchanges. It was one of the first big exchanges and it provides customers with a platform that is secure and easy to use. It was originally started in Slovenia but has moved its' operations to Luxembourg.
Bitstamp uses MultiSignature technology for its hot-wallet, as well as a fully insured cold-storage option where kept off-line. They also offer a number of other security features such as two-factor authentication and confirmation emails to enhance account security.
Bitstamp provides the option for limit orders, stop loss, and trailing stop orders. They have an easy to use API that can be integrated into user applications. T
Overall, Bitstamp is a secure and reliable exchange with good liquidity and a solid infrastructure. It is a good option for beginning traders as well as more advanced crypto holders.
Trading Fees: Tiered system depending on volume ranging from 0.1%-025%

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%

UNUS SED LEO is an initiative started by Bitfinex that is focused on increasing the exchange's transparency. UNUS SED LEO means "one, but it's a lion" in Latin. The iniatative was created to increase the transparency of the exchange's finances, following a controversy related to the allocation of reserves from the stablecoin Tether, that was created by the same parent company as the Bitfinex exchange, iFinex. It is built around a token burning redemption mechanism which is tied to the parent company's revenues. Their dashboard provides insights into the fees that are collected, and the LEO tokens that are burned.