I do it because I trellis my tomatoes, and if I didn't, it would be tomato insanity out there. Well, more than it already is. I have heard that cutting off the suckers helps the fruit that's on there to ripen more quickly, but I don't have any evidence to support that.
I pull of the bottom yellowing, unhealthy leaves that do not have flowers on them. I heard pruning away the non producing branches will help the tomato plant bare more fruit. I do not know if you need to do it.
I've done a lot of research on that this year. I was going for the single stem method. I tried to make sure I took all the suckers off and have one main vine. I wasn't quite as diligent as I should have been so a couple of my plants now have two big vines. I think that it has worked very well. I normally can't get heirloom tomatos to grow here and this year I have a ton of them on. I think that it's true that you get tomatoes faster and earlier if you prune. If my husband had his way our tomato plants would have no foliage at all.
I was also curious about other peoples pruning methods.
Because our growing season is so long here the tomato plants tend to get really really big (one of mine has grown 4 feet up the trellis, 5 feet back down, and 5 feet along the ground) so I like to prune off everything down to the biggest sucker near the ground when production slumps in the hottest part of the summer (pretty much right now, I've been doing this for the last few days.) I'm left with a pretty small plant, but it has a huge root system to support it and it grows really quickly to produce more tomatoes through our long, mild fall. I don't think this would be a good idea in your area Petey, since your season is just a tad shorter than mine.
Pruning depends on the type of tomato plant, determinate or indeterminate. I always prune indeterminate tomatoes since they're grown on a trilis. I let the determinate tomatoes grow as much as possible, usually in a cage since I don't have a lot of room to let them spread out on the groung.
We don't usually get a freeze until mid-November or December, so there's a long time for them to get big again. The giants plants don't produce well anyway, because they get less sun and air so there's a lot more bug and disease problems.
Mine are all indeterminate and they were...well...let's say they were pretty unruly. I cut them back to 2 main leaders and pinched off all the suckers and OMG, I had no idea there were so many tomatoes already on them! The things are HUGE, but I have plans for next year and I'm glad I did this. I have had veggie gardens before, but not much information. I am so glad to be here and learn stuff!!! Next year is going to be awesome!