You prune those middle stems when they are young, if your plants are too dense and/or want bigger tomatoes, otherwise let them. You will get more tomatoes but are going to be smaller.

You don't have to prune at all but it is a useful control technique. Each new sucker that grows will create a new growing tip. That tip will continue to grow in that direction and any new suckers from it later will become their own vines, and so on.

If the tomato is an indeterminate variety, pruning is more important because the plant will tend to out grow the pot if you don't.

You can stop any tip by pinching off the last bit of growth and it won't affect the fruit behind it. Just leave at least one leaf branch above and below where flowers/fruit will set.

Pruning will speed up fruit development also, useful for end of season frost concerns.

If, however, you see "determinate" in the variety description or on the seed packet, don't prune it at all. Determinate varieties stop at a certain size on their own.

I personally would not prune until it's bushy so they have some protection from the elements. If they are in a controlled environment (heat/light intensity) and you know what you are doing, you can prune suckers at this stage but they can easily develop issues doing this. Also since they are setting flowers, make sure they get the calcium/magnesium they need else you'll get blossom end rot.

I'm no expert l, but my grandpa taught me to prune the suckers from the ground up to about 8 inches, then allow 2 sucker to stay and mature (so you have 3 prominent stems) and then continue to keep suckers pruned from there up. I have a pretty good harvest of tomatoes every year, so I haven't questioned the guidance.

Always prune the suckers and all the laterals if you want the best fruiting. That is, unless they are cherry tomatoes, in which case just let them go wild.

You don't want more than one growing tip if you want really great tomatoes.

Edit: Most of the advice here is just terrible. Do what is proven by the pros. Rigorous attention to pruning laterals is the right way to go. People who say not to prune have probably never pruned properly so think what they do is OK. You need to do it every week before the laterals get too large or it affects plant growth. Just pinch them out with you fingernails as soon as they appear. Ignore the other advice. Thank me later.

I’m growing tomatoes for the second time and I never prune them unless there are yellow leaves, usually at the bottom near the soil, I just gave them water every other day!