When someone writes you a letter of recommendation, it is very important to write them a thank you note. Sounds like common sense right? Surprisingly a very small minority of students actually do it. Here are a few compelling reasons to write a thank you note to the author of your letter of recommendation:

It is the right thing to do
First and foremost, saying thank you to someone who has helped you out is clearly the right thing to

do. That should be reason enough.

Follow up requirement
It is quite unlikely, but the college/university that you are applying to might need to get back to your recommender for some reason. It is good to have a highly cordial relationship with your recommender in this case.