So I mod the r/pbp subreddit so I'm very interested in this topic.
My best answer is to link to the entries in the Play by Post Jam and the Correspondence Jam (70 games!) - both feature a bunch of cool games that were designed for asynchronous play. All of them by indie designers, I believe.
If you want a D&D version built for pbp, check out D20 Go - I've heard good things about it, though no personal experience. Of course, many ruleslite OSR games work well but they're not specifically designed for the medium.