Fallout 3 and New Vegas, ANY monster hunter game, Katamari games, Minecraft/Terarria.
I was writing a quick paragraph to describe why I play so much monster hunter (more than 2000 hours logged on MHP2G), when I realized it had turned into a full-out rant. If you're interested on my opinions on the best game ever made, check it out. Fellow fans, make yourselves heard!
Each one holds me for at least a few days at a time, even though I've played it for hundreds of hours before, but most of all is Monster Hunter, especially Monster Hunger Portable 2G. I would recommend this game over almost any other, if you still own a PSP. It's brilliantly done, very well paced - Other than that the learning curve goes from zero to sixty in the first hour or two, then levels out to a still tough but fair incline the rest of the game, mostly because at first you're just collecting pelts of small game, and then you jump right to dragons, since there's nothing really in-between dragons and not dragons, right? - the graphics are phenomenal, considering it's such an action-packed game for a handheld system. Sure, it's no cutscene from Crisis Core, but they're really good, and the design and style are fantastic; you never feel like all the weapons or armor pieces are even remotely cloned or repetitive. Along side a near-perfect combat system, the only flaw of which is that several styles rely on multiplayer combat systems, the monsters themselves are also incredibly diverse and unique, not to mention well designed and challenging.
This goes very well with a natural feeling crafting system for weapons and armor that takes all of five minutes to figure out if you ignore the tutorials; it isn't over-complicated, but nor is it over-simplified; it's both base and subtle enough that, if you want nothing more than better stats for attack and defense, then it's as simple as that; or, if you want to customize different pieces together for better or more diverse skills, this is available without too much hassle or simplicity. There are hundreds of items to use or combine, materials to farm from your environment, a feline companion that you can guide to be a fellow warrior, support, or even just monster-bait; the combat is tight, reflexive, responsive, and diverse enough to fit almost any playstyle, while still giving each style its own edge.
Overall, Monster Hunter Portable 2G is one of the most well designed and well executed games I've ever experienced. If ever you have the chance to play it, I urge you to do so.