I made a really great post about this before but it was lost along with half of my posts after all the pruning. I did manage to find the Sly Cooper portion posted somewhere on another message board, since I'm lazy like that and figured I would have done so. Anyway here it is:
I love the Sly Cooper series for most of the same reasons that I love all the Ratchet and Clank games. They mix traditional platforming with a different genre and blend the two in a way that makes for a unique and enjoyable experience. Where Ratchet and Clank mixes platforming and weapon-based combat, Sly Cooper mixes platforming with a less popular type of gameplay. Espionage.
By combining these two very distinct gameplay styles, you create an experience not found in another other platform game before it. Sneaking around as Sly (along with Bentley and Murray in the later games) you can do all of the basic things that master thieves do. Ducking past spotlights, avoiding contact with guards (or knocking them unconscious if that's your thing), stealing various items, and of course, making the getaway. All these and more, with a little bit of platforming thrown in for that extra awesomeness.
Although I prefer the Ratchet and Clank series over Sly, there are few things I'd like to touch on that I feel the team over at Sucker Punch does better than the guys at Insomniac. And that's the characters and story that goes along with the Sly games. Every single character, whether hero, villain (Dimitri is the greatest), or anti-hero has great depth and personality and seeing each of them interact with each other is very entertaining. That doesn't mean Ratchet doesn't have good characters too though. I just don't think they're as fleshed out.
Outside of the Sly Cooper and Ratchet series, notable favorites include various Sonic the Hedgehog titles (obviously) and LittleBigPlanet.