the biggest one is poloniex but it will require you to verify with documents and it is in USA. currently they are having a lot of problems with downtime and what they claim is DDoS and people lost a lot of money because they couldn't make any trades but price was going down.
the next one is bittrex but it also requires you to submit verification documents if you want to withdraw a high amount daily and i believe it is in US. it is smaller but still decent, there are a lot of altcoins on it like polo and it doesn't have as much downtimes. the API lacks many good features though
the others are small and usually don't have that many altcoins. the one that i can think of is btc-e that doesn't ask for verification unless you are doing a wire transfer. and it is outside of US (nobody knows where exactly lol). it has only a handful of altcoins but the volume is not that bad but the price is sometimes not compatible with the rest of the world LOL.
there is a similar exchange called c-cex with a lot more altcoins but it is much smaller that others.
there is also cryptopia which doesn't have fiat deposits but has many cool features and it is a small exchange considering the volume. and it has lots of altcoins.
there is another exchange which you probably will see be suggested after this in here called Yobit, i suggest staying away from it. you will save yourself a lot of headaches.