If they are green, healthy looking and not touching the ground, I would leave it be. The leaves/branches are important for photosynthesis where it converts light (sun) energy into chemical energy, then transfers it to the fruit that we eat. The leaves/branches also shade the tomatoes, preventing sun scald. If the leaves turn yellow or look diseased, they are no longer functioning. Those you can cut off.

It also depends whether its a bush or a cordon variety. Bush varieties should be left to do their own thing but with cordons the official advice is to remove all the side shoots. Whether you do or not is up to you.

I didn't think you were talking about suckers. The suckers should be removed as Steragram mentioned. The suckers are a new growing tip sprouting from the crotch between the branches and mainstem. My advice above is merely talking about normal branches with leaves.