Almost all begonias can be grown indoors with no great fanfare. There are some that need extra humidity so you will need to enclose them in some kind of container or humid environment. The only ones that I can think of that don't do that well indoors are the semperflorens (wax begonias).

Most begonias benefit from growing outdoors during the growing season but that isn't necessary if you have good light and pay attention to the needs of your plants indoors.

Thank you so much for the info hcmcdole!

Rieger begonias (Begonia x hiemalis) are especially nice for indoors because they are attractive and tend to thrive inside. Often you will see these for sale as houseplants. If you haven't had luck with other varieties, definitely give Riegers a shot.

Easy for Hcmcdole to say. Mcmcdole has the greenest thumb ever! I've been busting butt to keep my begonias alive this winter. I can't wait to see what happens when I get them outside this spring to see if they come back!