This is an interesting topic, since it is extremely important, and yet Scripture has very little to say explicitly about it. Recreation, in moderation, is not wrong. Sports as recreation and/or exercise are not wrong, in and of themselves. That said, a brief look at the world around us reveals many who have devoted themselves to the god of sports, and we would to well to take a lesson from them.
What are our motives? Why do we want to do the things we do? Is it to honor and glorify Christ, or to honor and glorify ourselves?
What is our focus? Does sports consume time that could be better spent? Time spent playing sports is one thing; what about time spent thinking about sports? Where does our mind go when we have a free moment?
These are not questions that have cut-and-dried textbook answers. We must seek God and search our hearts to find these answers.
Judson, you mentioned entering a competition; some hypothetical questions: What if you win? Would you move up to a higher regional competition? How would you feel about that?
What if you don't win, but show strong potential? Would that drive you to train harder to re-enter next year, if you see potential for placing better? Would you allow that to dictate your time management?
Something was mentioned earlier about the tendency for Sunday to be devoted to sports, instead of to God. I agree with this concern, but I'd like to expand it a bit as well. What are our lives devoted to?
Satan would love to derail our lives, by any means possible. Whether by inducing us to outright sin, or distracting us from the things that really matter, he is always at work (but "we are not ignorant of his devices" 2Cor 2:11b). May we seek the Lord, and find the wisdom that comes from Him. Harder perhaps: may we live according to that wisdom, for His glory.