I don't think that would be probable at all. If you have two varieties and cross them (or they cross by themselves), they will most probably poduce a cross. You will find it hard enough to cross two plants of the same variety (if they are crosses to start with) and get an offspring that's identical to either of the parents. Heirloom ones I think probably do produce offspring that are identical (since they have been around for a while), but of you cross them, they will change. On the bright side, an insect pollinating a plant will more likely pollinate a flower on the same plant, since it's easier to collect pollen from flowers of the same plant, don't you think? (I would think so anyway, but no guarantees.) :)

As for the self fertility thing, you'd get a much shorter list of plants that aren't self-fertile, so that's good news. Most plants are self-fertile. Some even have flowers that will each stay closed fertilize itself, apparently (tomatoes, violas, etc.)!

One plant that comes to mind is wild petunias. I grow them and collect seeds every year. I have all kinds of petunias, but these tiny ones (started from one plant) produce plants that are all the same except for slight variations in the value of the colors (light/darker purple/lavendar).

Biennial foxgloves come true from seed when planted with perennial types. Couldn't say with veggies, though. I don't save them.