It all depends on how committed you are, what your goals are, how good your trainining is, what your natural talents are, and how hard you work.
If you want to do this as a hobby, to enjoy dancing, to learn how to make your body do new things, to meet people, and to enjoy friendly competition, then it's never too late to start. There are amateur competitions for all age levels and proficiency levels. You can do it as a hobby, practice a few times a week, and have a great time.
If you want to get really serious, and strive for being a high-level amateur (like someone who competes nationally and internationally), then it's a lot more work, but it's still possible -- depending on what you've got naturally and what you're willing to put into it. One of the top amateur Canadian couples started when they were in college. They've worked very hard, and are beautiful dancers.
If you want to do this as a pro, like the teachers on "Dancing with the Stars," then you've got a lot more work in front of you and frankly starting at your age might be a drawback. Ashly and Cheryl, for example, were dancing well before they turned 10. However, that doesn't mean it's hopeless -- supposedly Jonathan started in his 20's, and he's developed into a great dancer through many years of concentrated full-time hard work.
The main thing is to get started. Once you get started, and learn what you're getting into and how you feel about it and what your aptitude is, you can set your goals. It's never too late to get started, because everyone starts from pretty much the same place, and you've got to start somewhere. The great thing about competitive dancing is that there are different levels and age groups so there's a place for anyone who wants to participate.
