If your budget is higher than "free", check out vBulletin, too.
If you happen to be hosted on a Windows server, an ASP forum may be more convenient. Snitz is popular, though I've never installed it. Sites like hotscripts.com can give you a lot of ideas for free and paid scripts.
I'd give an ogle at punbb, too - nice and lightweight (meaning fast fast fast! and not overloaded with features). My guess would be that it'd let mods get mailed - this is just 'subscribing' to a forum, which I believe is fairly common, or at least I've seen very, very basic forum boards with that capacity years ago already.