It depends on what you are looking for. I know a lot of commercial watermelons are grown from grafted transplants where the desired fruit type has roots that are very susceptible to disease so they graft that on to a variety with a more resistant root system. Tomatoes have been grafted to jimson weed (related genus - and hallucinogenic) with bad results. Apparently if you graft high enough on the jimson weed stem so it has leaves on it, the nasty suff will show up in the fruit. No leaves - no nasty stuff.
I actually do research on grafted apple trees and here the rootstock can have a great affect on the scion. It probably isn't worth it, but if you had a great variety that didn't grow well, you might be able graft the shoots onto the shoots of a more vigourous rootstock. Or if you had a variety that was prone to diseases, you might be able to graft it onto a more resistant variety. This last one is a large focus of what I do in apples - at the molecular level.