Pokemon! (SoulSilver and X)
I love all of the main series pokemon games, I didn't get to play any as a kid, but I picked it up in college (when I was old enough to understand the mechanics at work) and fell in love. I love completing the pokedex and breeding perfect pokemon to give away; it's a great way to kill time, explore a world and story, and challenge myself. I feel really gratified when I get a pokemon I've been trying for for a long time, when one of my favourites evolve, when I beat a difficult gym, etc etc. Pokemon makes me happy whenever I play it, so why would I stop?
Harvest Moon (any title)
Man, you talk about a slice-of-life genre done right. If you want to relax into a character and kill time living an idyllic country life, the Harvest Moon games are for you; although probably the older titles more than the newer ones. Newer installments in the series seem to favour a more frenzied, multifaceted approach. Instead of building up your farm and having a family, you must also defend your farm from enemies, compete with neighbouring entrepreneurs, sell your products yourself, resurrect structures or entire land masses, befriend/help the Harvest Sprites/goddess, make friends and solve their problems, et cetera et cetera et cetera! Definitely still fun though; I find most HM games are as hectic or relaxing as you want them to be.
Final Fantasy (yes, even the newer ones)
Cutscenes shmutscenes. I love immersing myself in a big, vivid story, and if there's one thing Square Enix does right it's that. I love the immersive graphics, the cool, outrageous, fantastical designs, and the multilayered characters. These games are usually long and have a great story payoff at the end, too; definitely a must for those who like a really strong narrative focus in their games.
Tales of Vesperia/Graces/Symphonia/Xilia
Everything I said about Final Fantasy, but with more ease of multiplayer and more focus on side quests/optional objectives? Yes please!
For some more specifics...
Pikmin
I'm paraphrasing, but GMR magazine once described this game as all the fun of strategic wargames, without the camo-clad angst of an RTS. Pikmin is fun, cute, motivating, and requires you to use your head a little. It's addictive and really rewarding when you make progress.
Avalon Code
Oh man, this game. Kay you know how most games you have to save the world, or at least part of it? In this one, the world is ending, and your job is NOT to stop it. No, your job is to find everything in the world that's worth taking to the next one using your Book of Prophecy, and rescue the Book Spirits before it's too late! There's a lot of customizing in this game too, because when you record ALL OF THE THINGS in your book, you can alter them with different codes; replace an 'iron' code in an enemy with an 'illness' code, for example, and he gets a lot weaker! Add a 'fire' code to your weapon and set things ablaze! With your weapons, armour and accessories, you can even code yourself entirely new weapons! The storyline also changes slightly based on your decisions, which I'm a big fan of.
Mario Kart: Double Dash!
I love this Kart classic. It makes me a bit sad that it's gotten dated and you can't bring it to a party expecting everyone to know it and its console anymore. It's easy to pick up and play, but not many are willing when there's so many more recent titles they already know. I love the doubles mechanic though; my brother and I were an incredible team and it's way more fun to play cooperatively.
Chibi-Robo!
You play as a tiny robot who works in a home by cleaning up messes and solving the family's problems to make everyone happier.
... It's really fun and addictive, okay? It'll turn you into a virtual neatfreak, obsessing over finding enough scrap-metal to make a ladder so you can reach that stupid stain on the wall, but it's very satisfying when you complete a challenge, and there is a pretty decent overarching story that plays out as you progress in the game.
There's probably lots more, I may edit/re-reply later :)
