I've been playing console games since I can remember. My older sister had a Colecovision, and the day she taught me how to play Cosmic Avenger started me on a path that led me to amassing a pretty large collection of games and consoles, ranging from that very same Colecovision to the Xbox 360. I grew up with games, and games have grown up with me.
What makes you want to play a game? On the older games, there was the drive to get the highest score possible. You would have showdowns in arcades and living rooms between players boasting their skills. Then, starting with the NES, there were games that had storylines (like Ninja Gaiden) that motivated you to play and see the next piece of the story, and there were games (like the Zelda and Final Fantasy games) that advanced your character with additional abilities and items that made you want to develop that in-game character to the fullest. There were also games that saw people taking out frustration by beating the crap out of enemies, like Double Dragon and later Final Fight and Street Fighter II. Those were always fun too.
What makes me want to play the games of today? I'm not a huge fan of online multi-player games, unless I'm playing co-op with some buddies in Borderlands or maybe an occasional Forza 4 Race here and there. I have a hard time playing a game with no depth that results in cheap kills by some 8 year old whose parents use the Xbox as a babysitter But in playing those on or offline, I'm always searching for the best weapons and armor, or the fastest tuning setup on a car. These games let you amass a collection of stuff to further customize the gaming experience. I love that.
In Skyrim (my current addiction) there is a constant drive for me to explore every cave, town, and fort in hopes of finding a better sword, bow, or armor than what I have. The story is cool too, but like the RPG games of my youth, I want to advance that character to the fullest. That's the same thing I did 25 years ago playing The Legend of Zelda. I also like the fact that you can play this game in small amounts. You can save it anywhere at pretty much any time, and for someone whose gaming time has been shrunk by that annoying thing called LIFE, I very much appreciate it.
Also, games can be expensive. In true GRM fashion, I have a rule: never pay more than $20 for a game, unless it's Forza. Hit up yard sales, flea markets, clearance bins, and even junkyards for games. You'll be surprised at the hidden gems you can find for dirt cheap. That copy of Skyrim I'm playing was $15 a few months back at a yard sale. It was complete and in perfect condition.