Warcraft III, which you've already said you guys play.
Garry's Mod, which I'm assuming you are counting as a Half-Life mod.
Titan Quest, personally, we like it more than Diablo III. It might not be better than Diablo II, but it's different. There's also now Torchlight II.
The rest of our games don't necessarily have bot support, but if they do, we usually don't use it even at a small LAN.
Star Wars: Jedi Knight: Jedi Academy - Tons of fun if you do Sabers Only and no Force Powers, but the game is still fun and a good bit different if you allow force powers and/or guns. The game has a nice rotational Dueling system which is a lot of fun and really intense, and even has a 2v1 dueling system. There's also free for alls, team battles, and bot support.
Rune - Less technically robust than JA in pretty much every aspect, but much more mindless and fun. A great game to boot up while people are getting set up, or during pizza breaks. People can jump in and out, smash eachother's skulls, respawn, and keep doing it. There are a bunch of weird game modes here, and some community patches add even more. There was this weard head-ball game where you tried to knock your opponent's heads into a goal or something... Super gory, super lightweight, and super fun. Great in-between choice. I don't remember there being bot support, but there may be.
Soldat is a surprisingly intense and strategic game once you get the hang of it. Give everyone jetpacks and knives and watch chaos unfold. Teams and bots supported.
Suicide Survival is similar to Rune in that everyone can pick the game up and start playing competently. It's so much more simple, though, and nevertheless gets super-duper intense. There are no bots, but four players can make a loud, rowdy good time. Just make sure you are the kind of people to talk smack as soon as you blow eachother up. (HL2 Mod)