Chillis yes, but sweet peppers, no, as these are annuals. Most chillis will re-grow again next year and flower and fruit if kept frost free.
I just wonder if it's worth the effort, though, as you can produce new plants so easily, even from a chilli bought in a supermarket, and these new plants always tend to be more vigorous.

They will, if protected from the cold, continue next year. I am able to plant every other year, and if they start to produce when you take them in, leave them on the plant, and they will continue to ripen very slowly. Keep them in an enviroment 50 - 55 F or above.

Thankyou both for the answers! You are right Bertie Fox, they are EXTREMELY easy to grow and I love the process of seed to plant. Why deny myself that?!! Also, Thankyou Wylieintheazores, that is good advice but the temperature is not something that I could sustain. :)

Because of the temperature requirements, that's why they usually go on the compost heap at the end of the year.