Basically you need somewhere to post and a method of generating random results.
First, I'd suggest Myth-Weavers [http://www.myth-weavers.com/] it's one (if not the) top PbP sites. They can handle most systems' character sheets and dice. I'm pretty sure it could handle anything you want from in, unless it's a really obscure system. I'm assuming you'll be running D&D, though so have no fear.
My second suggestion is RPoL [http://rpol.net/] (RolePlay onLine). The site is practically built from scratch specifically for PbP gaming (M-W runs a heavily modded vBulletin). It has nifty features, such as in-character private messages and such. It's still pretty good but I don't have much experience with it.
Finally, you can use any forum and a website where you can roll dice and share the results such as InvisibleCastle [http://invisiblecastle.com/roller/]. Also, you can do the same in emails, if you wish and you think it'd be more convenient.
