Contrary to popular belief, tomatoes do not produce suckers. Many gardeners will no doubt be shocked to hear that, because they were always told they had to remove these suckers. But a sucker is, by definition, a stem that doesn’t produce fruit. So-called tomato suckers (if allowed to grow, at least) will produce both flowers and fruits.
These “suckers”, which grow from the leaf axils, are simply secondary stems. Studies show that unpruned tomatoes produce more fruit than pruned ones, although the fruit may be slightly smaller. Still, there is a net gain in total tomato production by weight, so you get more “tomato” to eat by not pruning … sometimes considerably more (under good conditions, unpruned tomatoes often produce twice as many fruits).
“Now wait a minute”, I can hear you saying, “won’t those suckers sap my plant’s energy?” No, quite the contrary. Secondary stems bear green leaves and everything that is green on a plant carries on photosynthesis, that is, converts sunlight into energy. So, these supposed “suckers” actually give the plant more energy.
It is hard to attach more than one tomato stem to a stake, so if you stake your tomatoes, by all means prune out any secondary stems you can’t handle … just don’t call them suckers. If you use a tomato cage, though, and these days most gardeners do, it will support the secondary stems very nicely and you don’t have to prune anything … well, at least until the end of the season, when it is worthwhile pinching off late-season blooms that won’t have time to produce mature fruit. But leave green foliage on the plant as long as there are still tomatoes to harvest.
Removing suckers: yet another useless task the laidback gardener skip!
For further details, here’s a more in-depth article on the subject: The Truth About Tomato Suckers.