I'm not really qualified to talk about what makes video games good (since I tend to play a lot of crap) but for me to call a game good, it would have to be something that's engaging.
If it's a single player game, it has to be interesting to the point where I don't want to stop playing. I want to find out what happens next; if I don't care, I'm not drawn into it, and if I don't care, then my attention and interest won't be there for long. I'm also a huge fan of side quests and little rewards. Get 50 kills with this weapon, and you'll unlock something new. I really like the weapon rankings in recent Call of Duty games, where if you use a gun long enough, you'll unlock attachments and what have yous. I'm a huge completionist, so this stuff is really cool to me.
In multiplayer games, I love it when I can track my stats, but I'm not interested in anything too in-depth. I like knowing how many kills and deaths I have, how many assists, headshots, accolades, and I love knowing how many kills I get with certain weapons. It gives me a good reason to try out other weapons to get my rankings for them higher.
My top three most played games (according to my Raptr page) are RuneScape with 2,799 hours tracked (probably 1000 more hours untracked) Combat Arms with 769 hours played, and Call of Duty: Modern Warfare 2 with 198 hours played. The big reason these games have insanely high hours played is because I genuinely love playing then. With RuneScape, level progression was really fun, and it was done in a way that felt rewarding to me. The drive of going for a level 99 skill was worth the grinding. In Combat Arms, the game is VERY fun to play (at least to me) and I love trying to hone my skills and increase my KDR. Modern Warfare 2 is the same pretty much, except there's more of an emphasis on unlocking everything, which is one of my favourite things about video games - unlocking things.