Jeez, tough one to answer. I have so many mods on my forum (that I use all the time) it's difficult to say, but I'll have it a go...
1.
Email All Users = I modded this a bit to accept HTML messages and now use it to send out newsletters (the newsletter mod time's out on me). I also send out passwords for events weekly to my members, so again, this mod was a must.
2.
Private Messaging = For obvious reasons.
3.
Calendar Mod & Shout Box (This one's a tie) = I have weekly events every Saturday, so the calendar is a must to keep all my members abreast of what's coming up and where. The Shout Box mod is new for me and I use it as a "Forum Announcements" mod. I could not get the Alert Mod to work, so this one suited my needs just fine.<