LDraw.org hosts 2 monthly contests.
1. Model/Scene of the Month
Using LDraw, create a model or a scene. Fairly basic, but it's turned up some interesting results. There's no prize for this one except for the illustrious glory that will doubtlessly ensue.
2. Part of the Month
If you create a new part in LDraw, you can enter it into this contest. Fairly standard, this contest follows the model of the the former.
Thanks again to Bruce N H for the tip!