Chibi-Robo

Chibi-Robo is a very amusing little adventure-platformer (heavy on adventure) game for the Gamecube. The basic premise is that you are a tiny robot whose duty it is to serve a family - and of course, the family is lovably dysfunctional. Not only that, but all of various stuffed animals, action figures, and the like are alive, and usually even more dysfunctional than the humans - the disturbingly nectar-addicted teddy bear, for example, really takes the cake.

Anyway, the actual gameplay consists largely of fetch quests, platforming (often in the form of exploration), and timed minigames. These are quite entertaining - the platforming is aided by the ability to hover briefly, as well as the ability to move around various blocks. You are limited in your ability to explore by your energy - your every action drains Chibi Robo's energy, which can be recharged by plugging yourself into the wall. You also are limited by the day-night cycle, which changes relatively rapidly. The people and other denizens of the house do different things during the day and night.

Your two currencies are a basic form of money, which is used to buy various things to aid and enable exploration, as well as power a very plot-important robot, and your family's love, which increases the amount of energy Chibi-Robo has. These are accumulated not only by doing various quests, but also by mundane things like taking junk to trash cans and wiping up mud. The game, funnily enough, actually manages to make cleaning fun, by offering an immediate reward of one or both of these currencies, which have quite tangible effects in the game.

Beyond the basic game mechanics, the sidequests are intriguing enough to keep you wanting to do them (especially since many of them are accomplished by exploration, taking you to fun places), the gameplay fun enough, and the characters quirky enough to really keep you interested. On top of that, the setting, a house, is a rather odd one for a platformer, and the possibilities for exploration within it keep you going.

To sum up:

-Quirkiness is good, especially if fetch quests are a large part of your gameplay. If you have relatively standard gameplay, spice up the setting and the characters.
-Unconventional settings can work quite well, especially for platformers and adventure games. Having a main character that isn't human lends itself quite well to this, so don't be afraid to run with it.
-This may seem basic, but exploration is plenty compelling if you know that you'll find things in nooks and crannies. I'm not saying that every game needs exploration, but there's a reason that adventure games still exist, even if they're a bit rarer than they used to be. This game is a great example of compelling exploration.