I own a few board games and play with friends every few weekends.
Some personal favorites from my shelf:
Samurai
https://boardgamegeek.com/boardgame/3/samurai
I've got this old school version of the game. The newer releases have different graphical design.
The rules are quite simple (except for the mildly complex rules for tallying points), but it's very deep once you get beyond the surface.
Ivanhoe
https://boardgamegeek.com/boardgame/883/ivanhoe
A good mix of "take that!" and risk assessment. You draw cards all the time, so it's got a big random factor, but there's a lot of tactics in whether or not to expend the cards you have quite yet, since you can play as many as you want any round, but only draw 1.
A few well known games I also really like: Carcassonne and Timeline.
Also worth noting: Samurai and Ivanhoe, plus several of my other favorites are from the same designer: Reiner Knizia. He's made so many good games, including ones that I've played but haven't bought yet. For example:
Tigris & Euphrates
Through the Desert
Ra