I took the GMAT three times and scored 620, 640, and 580 respectively. In between attempts I did my best to do focused test prep, but each time I feel like my scores were across the board. The last time was particularly brutal because I didn't get much sleep the night before, since I was worried about my performance.

I am willing to take it again but my confidence is shot. Any suggestions for me? Should I try to take the GRE? I've heard that it's an "easier" test.

Barring that does anybody know of any MBA programs that would accept me as a candidate with my current scores?

The right schools depend on the rest of your profile. Take a look at
GMAT Tiers - strong schools for your GMAT www.find-mba.com/board/27082
Shortcut to find the best US MBA www.find-mba.com/board/36065
Why you should take the GMAT http://www.find-mba.com/board/38939

I agree with Duncan. The admission to B schools will depend on your entire profile including academics & professional experience rather than just GMAT.

As far as retaking GMAT is concerned you first need to analyze the sections where you need to focus and then how much time & efforts you can devote to the preparation; accordingly take a decision.

Ok, I guess I'll have another go at it. Thanks.

If you are looking to take the GMAT again, there are some common GMAT studying mistakes that you might be making and if so, should correct them.
1) not taking notes: people remember things better when they write them down
2) note reviewing answers: the best way to improve is to analyze your mistakes, so any time you do practice problems make sure to go over the right answer and the best way to get it
3) not building mental endurance: the final, and most important last step is to get your brain used to concentrating for 3.5 hours by taking full-length (including AWA and IR) practice tests