Yeah in our garden we plant chili peppers, Anaheim, jalapeno etc. Tried replanting seeds one year, and while the fruit looked (mostly) like the parent plant, the heat was all over the map. It was chili roulette!
I had a few Franken-squash take over my garden one year. They even seeded themselves. The place I order seeds from will even warn you if the peppers can be cross pollinated easily.
Yeah...I've had some really odd 'volunteers' come up the year after planting mixes of squashes. Melons are are apparently notorious for crossing as well.
According to a professional pepper farming acquaintance, if you do this for a couple of generations, the heat mostly disappears and the taste becomes bland. They go to some lengths to prevent cross-pollination.