seeds from hybrids will usually not come true, but they should grow. You will probably not get the exact fruit that the seed came from but it will still be fine.
I have saved seeds from tomatoes etc. and they have grown just fine and produces nice tomatoes.

Thanks...so when you say that it will not be the exact fruit that I got the seed from, do you mean that it will be a smaller version or just funky looking?

lol! not funky looking, just not the identical fruit. You probably wouldn't even realize the difference.

There are all kinds of seeds available in the grocery store. I have some seedling peaches from the store and they have made at least one winter, so they are hardy here. Cabbages will root and make yellow flowers with long pods of tiny black seeds. We have a nice line of tomatoes we have saved over quite a few years that came originally from the store and had additions as the bees got busy. Apples work well too and some turn out VERY tasty.

I too have grown many plants from grocery store seeds. One thing to be aware of with peppers is that they are ripe. Most sweet peppers in the grocery store are green in colour and not mature. For pepper seeds to germinate they must be from red ones. As for hot peppers I have grown habaneros from grocery store fruit, as well as some called Jamaica hot, but the Jalapenos which are sold green in the grocery store are not mature. I have never seen red Jalapenos in the grocery store, but they do turn red when mature. I would test a few of the seeds you have by germinating them folded in a damp coffee filter placed in a baggie on top of your cable box. They should sprout in about ten days.

Yes they do grow, but many will probably not grow true to form, for example like meyer lemons. Most Asian peppers will grow true to form. I've done it.

Beyond seeds, you can grow such things like pineapples from the tops a pineapple. Once the plant produces a fruit though the mother plant will die..