Facebook Rules (Updated Page Terms)
It is true you CAN now run a contest on your Facebook Page and ask people to comment and/or like a post for an entry. This is a new change from a few months ago when this action could have got your business page shut down.
Being a user of apps, I would rather just use an app and have the data collected for me. However for all those non-app users out there, now you too can participate in the contest game on Facebook.
You can also use likes to vote, or have users message you or the Page as an entry, and more.
Something I did not know that I found interesting is that it is NOT ok to ask people to tag themselves in pictures of a new product in exchange for a chance to win a prize. However you can ask them to submit names of new products in exchange for a chance to win a prize.
Interesting and never boring.
Information interpreted from Facebook Page Promotion Terms: