Google's John Mueller reluctantly explained in a live webmaster video this week on YouTube at the 31:22 mark that he would "watch out" when using contests to get links. He said the links might not be "clean" and if you are doing it to "exchange something" that is against their link guidelines.
So if you tell people to link to you as part of the contest, that would be against Google's guidelines. If they can win and part of the contest encourages or requires a link back to your site, that is against Google's link guidelines.
John said:
I think the situation where you're doing kind of a contest is something to watch out for. So, mostly with regards to whether or not these are actually clean links or not. In the sense of are you perhaps exchanging something for these links like do you require a link in order to take part of the contest.
But if the contest doesn't require this and you do it like maybe the SEO Hero thing, where they just get links because the contest is out there - then I assume that should be okay.
As the Google links schemes page says:
Buying or selling links that pass PageRank. This includes exchanging money for links, or posts that contain links; exchanging goods or services for links; or sending someone a “free” product in exchange for them writing about it and including a link.
So it can't get too close to that.
Here is the video embed:
Forum discussion at Google+.
