Most common diseases can't be "cured". Many can be slowed down and managed so that you can bring in a harvest.

Some diseases affect fruits, some do not. It can depend on how systemic the disease is (as in the case of viruses) or how severe the disease is. Many spots on fruit are pest damage that are mistaken for disease as well. But some diseases just don't affect fruit just because that's not how the disease organism works. Some affect the fruit only cosmetically, and the fruit can still be eaten and will taste fine--so the market grower may pull those plants, but the home grower may try to manage the disease until frost.

When to pull depends on a lot of factors. In general, I would say--always pull anything with late blight because of how quickly it kills, how easily it spreads on the wind, and how destructive it can be not only to to tomatoes but to potatoes as well. I would also pull any viruses that stunt the plant seriously and ruin fruit, especially since many common viruses have no cure, cannot be slowed down, and often can spread to plants other than tomatoes. Viruses and some bacterial diseases also necessitate controlling the pest that vectors them.

As for your plants--do you know what they have? And are you taking the right steps to control/manage that problem? Because it's impossible to know whether to pull those plants without that information.

I'm not sure what they have. I tend to call anything that puts spots on my leaves or spots on fruits 'blight'. From the description of late blight, I'm not sure I've ever had it in the 10 years I've gardened. Is it common? It seems like at a minimum I should figure out how to distinguish late blight from other issues if it's that serious.

In the absence of being able to categorize the exact disease, I was hoping I'd get some rules of thumb, such as when it spreads to the fruits, it's not going away and when in closer contact with other plants get rid of the plant.

Late blight is not common, no. There was a devastating outbreak back in 2010 that destroyed tomato crops all over the place, though. Where are you located? If in the US, you can track outbreaks on usablight.org. There are also tons of sites online that document the symptoms of late blight.

srj19: In the absence of being able to categorize the exact disease, I was hoping I'd get some rules of thumb, such as when it spreads to the fruits, it's not going away and when in closer contact with other plants get rid of the plant.

If only life and growing tomatoes were that easy. You need a diagnosis. If you don't know what it is, you're groping in the dark. Most foliage diseases will spread to nearby plants, but appropriate controls can delay, slow down, or prevent that spread. But if you don't know what it is, you don't know what the appropriate measures are. Foliage diseases of tomato are so common that if people routinely pulled plants just because they were close to other tomato plants, regardless of what the disease was, almost nobody would harvest any tomatoes ever. I suggest you contact your county extension office to get help with a diagnosis and recommendations for action.