I have been to dozens of tournaments over the years. I have even done quite well (2 years in the top 10 nationally for kata and weapons kata). But now I haven't done a tournament in years and don't really feel the desire to. Below are my list of pros and cons of tournament play.
The best thing about fighting at a tournament is fighting someone who you don't know. It's a great way to gauge your abilities in that way.
You get a chance to see other schools and styles of martial arts. This can be a great learning opportunity.
The opportunity to be competitive and win a trophy can be a great confidence booster as well.
Most of the fighting done at tournaments is point fighting, which is more of a game than a fight. The effectiveness of a technique does not count, only that the technique made contact with a legal target area. This could give people an untrue view of their effectiveness.
Many judges prefer "overly dramatic kata." In a kata a martial artist should have complete concentration and be level headed. At tournaments you see people who look and act angry during a kata, which is seen as dramatic and often loved by judges.
Many other dojos are overly competitive and place all value on tournament wins.
With all that said, I do think students should at least see a tournament during their martial arts journey at some point. www.Krane.org is an organization that runs all of the reputable tournaments in New England.