You have to smart about the contest you run! I have seen posting contests go crazy because people just spam the forum with short, low-quality posts. I personally have never held a forum competition, but I did hold some raffles on my blog as well as my YouTube channel. The trick is to make the contest fair and not too hard to enter. If done right, competitions can be very successful.
I think that could be really good for your site. There are a lot of competitive people out there who I'm sure would love to do something like that. Especially if they are able to win something. That might also be another way that you can get more people on your site. I'm sure that if enough people were super excited about it then they would go and tell their friends they should also sign up and try it out.
When our office website was wanting in hits, we launched a contest that involved fans of local actors and actresses. Our site had a heyday with the floods of entries for the contest that was actually a mock for the awards night. Who do you think is the best actress? Questions like that were answered in droves and we had to hire a staff to do the compiling of entries. And when the results were published, the expected protests came. Not content with the site, those complaining even called us on our landline. It was a great activity that injected power to our site.
I almost forgot. We have an ongoing competition but not exactly for the forum. It is a contest on short animation of local legends and myths (native to the Philippines). Mainly intended for students, the contest requires an entrant to choose from the given list of legends and submit a synopsis before going to the animation proper. And there would be a sort of workshop before the entry is finally accepted. I am not well versed with the contest rules because somebody else is handling that. But nevertheless, queries can be posted in the forum so we get a higher attendance now.
Right now I am still starting out so no, I haven't. I think that this would be a good thing to do though. I'm sure that you might also be able to get more people to come to your page too because people would want to do that. I have heard of people doing this with their page so that more people will join. I totally want to try something like this out though.
You are asking all the things that I'm thinking about asking so far. This forum used to have contests going on before it stopped working for a few days. I personally did not join, but they were a little compelling
I don't have any competitions running on my forum at the moment but it is definately something that I may consider in the future. The problem with this is that you have to invest a lot of money as prizes otherwise not many people will bother taking part in the competition. This can be difficult sometimes especially when you've put quite a bit of money into the forum already but it could also encourage more activity so it good be beneficial for you in the long run