I would like to offer a paid webmail service on a domain that I own; can anyone recommend an open source | freeware program that I could install, which will offer a fairly stable product?

BTW, if you are tempted to ask why would anyone pay for webmail when there is no shortage of free services (gmail, hotmail etc), let's just say that the domain is interesting. For instance, if you were a plumber and could get a site that could give you an address such as joe@plumber.com, wouldn't you want to pay five bucks for it every month?

Check out RoundCube.

I second roundcube aswell. I use it for webmail host as well. It runs well, and some good features.

We have three different services installed on our servers (SquirrelMail, Horde, and RoundCube). I personnally like RoundeCube the best. I think it has the most options out of the three we use. It even uses keyboard shortcuts, which was really impressive for me. Hope this helps and good luck!

You could also try http://www.afterlogic.com/products/webmail-lite

I have this running as well for a client. I prefer roundcube, but it is nice aswell.

I would suggest RoundCube and SquirrelMail.
Most people prefer RoundCube but i personally like old-school SquirrelMail :P

I definitely suggest roundcube, lots of good experiences with this webmail client!

+1 for roundcube and Squirrelmail. DO not opt for horde, Had a lot of issues with horde lately.