I enter about 5-6 beers per year; usually 1-2 per competition. If I have something on-tap that's tasting very good, and it was brewed true-to-style, I'll find a competition coming up shortly to enter it in. As others said, the feedback is awesome, but take it with a grain of salt. I once sent two beers off to three competitions to see how the scoresheets would compare. Here we're the scores from the comps:
Imperial IPA: 19, 38, 43(BOS)
Blonde Ale: 25, 36, 41(1st)
Lord knows how a beer that averaged 40.5 between two competitions scored a 19 at another comp. I bottled all 6 bottles from the keg at the same time. For Blonde Ale, I threw out the high and the low, and figured it was a 36-37pt beer. The point is, judging varies at different comps due to a varity of factors. Take the results with a grain of salt.
With that said, definitely enter comps. It's the best source of non-biased feedback you'll get, generally from people that have a good palette. It's also a fantastic way to fine-tune a beer. If you have a recipe you like, submit it to a comp. Review the scoresheets, make some changes, and re-submit it. I've done this with a few recipes that now consistently place, if not win their category in every conp they are entered.