I'm sure a lot of users do this already but don't admit it.
Nonsense. its not practical because of the time taken to withdraw cash from exchanges. Any arbitrage opportunity is quickly filled by market forces.
I know people who did this with a profit. It's especially profitable if you convert to other currencies as well.
Do you know which websites are best for this?
Right now it's not the best time to do this because of big swings.
BTC goes up and down by 100$ each day so you can earn without arbitrage.
When a price is more stable it can be profitable. Example - Mt.Gox USD price is always higher than other exchanges, if you buy on btc-e or bitstamp and sell on gox you have instant profit, but as others wrote here, the withdrawal time is long so it may take weeks before you get your fiat and can buy again.