David, I don't think there is a "should" in this case.
Here in the UK we do prune the laterals of our own cherry tomatoes, both under glass and in the open, but that's really only to save us the effort of providing support for those laterals - some varieties of cherry tomato, particularly the ones that have trusses of dozens and dozens of fruits, produce simply amazing amounts of growth that need really robust support. Also, to make sure the fruits ripen really well given our pathetic British light and sunshine levels, pruning helps to get plenty of light into the plants. However, I'm sure that pruning reduces the total weight of the crop we get.
Presumably you're growing yours outside. I think you can choose to prune or not to prune, depending on whether you want neat and easily controlled plants but probably a rather lower total yield (pruning) or maximum yield but plants that will sprawl rampantly even with strong supports (not pruning).
I'm hope you'll forgive me for changing the title of this post (from your original "Vegetables")!