Recent scientific studies indicate that humans do not mature completely in the reasoning portion of the brain until the age of 24 or 25 in women, and 26 or 27 in men. It stands to reason, then, that in a decision which will last not only this lifetime, but through eternity, waiting until these ages is wise. 
On a personal note, I was sure I'd found Mr. Right at the age of 19. (He was 21.) We were divorced soon after the marriage because we both changed too much to stay together. I recommend now waiting until the ages first suggested, which I did the second time, and have now been happily married for 30 years.

Sara, It is a common misconception that the Church encourages people to get married at a young age.  
 
I have been married for 2.5 years now, I got married when I was 23, my wife was 21. A little bit under the 24 & 27 Ages that Nicole referred to.  
 
There is no set age that the church says that you should be married by, I had a man in my ward serve in the Bishopric (Comparable to Clergymen) and he was unmarried until he was about 45.  
 
Hope that helps!

Most Mormons get married in their 20's. Many find that after their 20's it becomes much more difficult to find a mate. 
 
There is a strong emphasis on marraige in Mormon life, so Mormon leaders frequently and strongly encourage people, especially men, to get married as soon as possible.

This is really a personal opinion. My parents got married at the age of 18 and 19 and they are still married 17 years later. but then my grandparents got married in their early 20s and are still married 40 years later but it's more of getting to know the person you want to get married to and to pray about that person until you get an answer from our heavenly father.