For the next three days (today, Wednesday and Thursday), 1UP will be giving out 500 codes per day. First, you have to register with them if you haven't done so already. Next, check their LBP minisite for their question of the day. Once you figure out the answer, head over to Sack_Boy_1UP's page and send him a private message with your answer. The first 500 people who send in the correct answer will receive a beta code.
GamePro has 1,250 codes to be given away on Wednesday, October 1st. You must also register with GamePro in order to enter their contest. When Wednesday arrives, check this page out and enter your information for a chance to win. Don't enter your information till Wednesday though, the current page is for Monday's contest. Winners will be notified on October 2nd.
Source -- 1UP
Source -- GamePro
[Thanks to everyone who sent this in!]