My friends like to have small LAN parties, but they only want to play Starcraft and Warcraft 3, and I'm getting sick of RTS games, but none of them want to play any FPS's, the other obvious choice for LAN's.
Any one know any good non-RTS, non-FPS lan games? Preferably free or cheap, because most of us don't have a lot of money to spend.

Street Fighter?

Going to have a hard time finding a 4 player co-op game without spending any money.  If you aren't averse to MMO's get Dungeons and Dragons Online.  You can play it for free and with friends it's a lot of fun.
 
Either that or something like Titan Quest.  You can pick up the bundle off of D2D right now for cheap.  Maybe League of Legends.

I have been absolutely LOVING Unreal Tournament 3. I know I'm kinda late with it, but it's soooo much fun. Especially Greed mode; I love shooting dudes to see shiny skulls as big as you pop out of them. I don't even have an amazing PC, but it runs at almost 60 fps on all max settings.

 Dungeons and Dragons Online is decent and I dislike MMOs. I play it with my brother from time to time. Are there any decent online co-op pc games in general?   
 
If your all into rpgs check out Neverwinter Nights 2. It's pretty cheap now and you can play any of the modules on LAN.

I know you said non fps but counter strike in a LAN is pretty epic

I used to play Diablo 2 and Baldur's gate 2 on a lan.
 
Also neverwinter nights 2, but we installed the expansion and everything bugged, so we left that one.

Command & Conquer games? Red Alert 2 is great on LAN and must be cheap now. Or why don't you download the original C&C classic from EA. That's Free!

When we'd have lan parties we'd always play Diablo 2 and Serious Sam. Serious Sam: The Second Encounter is fucking crazy with like 5 friends running around. 

" I have been absolutely LOVING Unreal Tournament 3. I know I'm kinda late with it, but it's soooo much fun. Especially Greed mode; I love shooting dudes to see shiny skulls as big as you pop out of them. I don't even have an amazing PC, but it runs at almost 60 fps on all max settings. "

Diablo 2 is perfect for LAN if you're 2-4 players.

I would also go for borderlands. the 4 pack on steam is $90 which ends up being 22.50 a piece. 
http://store.steampowered.com/app/8980/
 
The whole game was a blast. 

trackmania

mario kart 

any fighting game

metal slug hotseat (can be real fun on the later levels)

guitar hero

I'd go for a Command & Conquer Game!! Can't go wrong with a bit of Red Alert 2 or so.

Altitude is very fun, but you need internet access for authentication purposes. perfect for 2-6 players, and it also has bots.

If you and yer bros have half life 2, check out some of the mods. Some of them can be really addicting. For example...
 
Suicide Survival 
Suicide Barrels
PVK2
Synergy
Rocket Crowbar
 
Just to name a few. You could always play half life deathmatch as well. Cant go wrong with toilet throwing :P
 
Edit: I am aware Half Life is an FPS. But its good fun!!!

Diablo 2, Titan Quest, are good ones. I believe Civ capable of lan games as well.