Off the top of my head, I'd have to say Skyrim, Minecraft, Terraria and Starbound.
For Skyrim I played the game constantly on release on the Xbox, I must of put 4 months into it before I put it down, but once I got it on PC I stuck to normal mods, graphical upgrades, magic mods, I even remember downloading the Naruto jutsu mod, but nowadays I usually install things like lovers lab, defeat and depending on my mood, either vampire or werewolf overhauls,
Minecraft I also played way back in the day when it was alpha and breaking a block to let water free could flood the world, I can't even imagine how many hours I've put into it since then, but now I just can't play it without mods, Pixelmon/Cobblemon, Thaumcraft, Blood magic, Astrological sorcery are some of my favorites, I also quite like the Jenny mod and hope they start working on it some more.
Terraria is also another game I've been playing since release, I put about 700 hours into it before I discovered the mods, now I can't touch it without them, Calamity and the DBZ mod are my current favorites.
And finally Starbound, while I didn't pick that one up until a couple years after release I never got super far into it before I started using mods, mostly LL mods like Sexbound, Critterbang. Teratophila, there's also a mod on the Steam workshop I really love, it lets you play as a highly customizable feral dragon with unique leveling and abilities that has multiplayer support, it's a lot of fun for sure.