We tried contests (Add contests on blender exchange), however after the first one we didn't get many entries.
It seemed to me that there was interest, but people didn't have enough time to put something together in their spare time in-between answering questions ;). At least that was what happened to me :P
If this is true, what about having something more like photography.se's continuous contest?
This would allow everyone to enter on their own time.
I assume we can't (yet) feature the weekly winner on the main site (in a banner or something), but we could have a "hall of fame" meta post like photography.se where the winners are collected, and perhaps we could feature the winner of the week in the question for extra visibility.