I tend my tomatoes to remove bottom growth and thin them out by removing suckers. I might run an experiment where I actually tend a single vine up a pole and remove every sucker. That is what you see a lot in books, but I rarely have that much time. Here are two pictures to show you what a sucker is, so you can decide what to do with them. I suggest removing some.
|My Finger is Pointing Directly at the Sucker.|
|Removed! You can See the Nub.|