yes you can I have done this with bell peppers. they dont all end up looking like the parent, as many are bred for a particular feature but the seed has other features in them.
make sure the fruit is ripe , red or fully yellow/orange for the other peppers. grow in good compost just covering the seed with compost. keep warm and germination should be through in a couple of weeks.

yes you can, but most of them won't come true as they may be hybrid,however if you go to farmers markets or organic shops and get them,you will have a better chance of a good crop,locally grown garlic is another one you can plant with agood result.

Oh great! I already have some cayenne peppers on the go but bought them as seeds from the shop, and wondered if there was a cheaper way to grow chillies and peppers. I've been looking up on growing garlic so I will definatly have to try that.
Does it work the same for tomatoes too?

same thing with tomatoes,you wont always get the same as what you have bought,but sometimes getting1 plant from the shop and saving the seeds from the crop you get works out cheaper than buying a packet of seeds if you only want a few plants,save the seeds and they will last up to 3 years.

Cool, will have to have a dabble with those as well. Thanks for your help :)

With tomatoes, though, you need to thoroughly wash all the jelly off of the seeds, or they will be very slow to germinate. The easiest way is to let the seedy goo ferment for a few days--that lets it liquify and detach from the seeds.

Thanks for the tip, I could see myself getting slightly annoyed trying to get just the seeds!