A great way to learn and find ideas. Some of these also have mini-games such as post-processing challenges, which is a wonderful way to learn about the different creative ways you can post-process the same image, and what you like best. The smaller and tighter the community, the more likely you will get better and more in-depth critiques.
Reason to be cautious:
Beware of scams. (These are typically of the form "Congratulations, your photo has won a prize! We're publishing a very expensive book of the prizewinning photos, would you like to order a copy?". Of course, every entrant has won a prize...)
Watch out for the copyright clauses; by entering, you may be assigning all rights in your photo to whoever's running the competition.-
twitter.com/dailyshoot - an archive of a daily social game that went for 690 days.
panachallenge.com - targeted mainly to Panasonic users.