It depends on the site.
Two years ago I used the now defunct betonsports, and they required an email/fax copy of your DL, a signed letter, and photo ID. After you did that, they'd pay out anything over $50 by money order.
Last year I used bodog, and while Bodog required basically nothing to create an account, if memory serves, they wanted you to jump through 50 hoops to get the money out....which irritated the piss out of me. They wanted faxed copies of stuff (who the hell uses a fax in 2006?) for every withdrawal.
This year I've been using sportsbook. Their straight odds tend to run a little behind bodog, but their parlays are bar none (even paying out on slightly missed parlays) and theres no red tape to cash out. You get one free cashout a month, each additional is $40....but unless you're winning a nice $2k parlay, what's the rush? They pay by check, and I've cashed out twice and gotten it within the week.
I personally prefer as little hassle and as much anonymity as humanly possible, so that's why i've settled on sportsbook......but if any of you have suggestions, I'd love to hear them.
edit: And sportsbook allows you to still use your Visa card directly, and last I checked bodog did as well. The only faults in that are based on your state of residence and your bank.