3 players on average?
Pretty much any of the Arkham Horror family of games will do.
Akrham Horror itself is a nice co-op game about killing Lovecraftian elder gods. It is a massive game though and takes a decent time investment (I think 90mins minimum, but it has been a while since I have played)
Elder Signs is a small game that crosses yahtzee with Lovecraft and is also co-operative. It works best with 4, but it plays well with any number of players from 1 to 8.
And then there is Mansions of Madness, a semi-cooperative storytelling game. It is kind of like a role-playing board game in that one player is the keeper who picks a story scenario they are running and plays the antagonists while every other players play an investigator who explores the mansion. The game supports 1-4 investigators, but there is next to no reason why one player can't play more than one investigator (one scenario introduces a hidden loyalty mechanic, but the general consensus is that one is kind of ass and unfair anyway). There are some problems with the game though. It is big, it is kind of expensive and there are a lot of eratas and rules clarifications to keep in mind. It is not terrible, but there is enough there to turn some players off of it and it is a bit of an investment. Also, it does not travel real well.
And then there is also Catan, Carcasonne, Puerto Rico. Pretty much the Eurogame standards. Some people really like Agricola. It is a complicated farming game that requires a lot of strategic thinking, but it has a way of frustrating players. Approach at your own risk.
The one other thing I will say is that if you have a group of 4-6 people who like playing board games, you can do nothing better for them than buy a copy of Battlestar Galactica the Board Game. So much fun and requires no knowledge of the show to appreciate. The big problem though is that it is balanced best for a 5 player game and everything else will leave you wanting.
I will leave it there for now. If you want more suggestions or need a different style of game, I have more. I kind of like board games a bit too much.