I had a different answer prepared yesterday but I forgot what it was. (EDIT: It was supposed to be Super Smash Brothers Brawl. Oh well.) So I try again:
The Super Mario series has, in my opinion, only been getting better as time goes on. Consistently strong, consistently innovative, consistently fun. Super Mario Sunshine is somewhat looked down upon by many gamers, but undeservedly. True, its a very green-political game (the main plot is that Mario, after a case of mistaken identity, is charged with cleaning up all the pollution from Delfino Island using no more than the sentient squirt gun he found) but quite frankly it gives the game a more interesting structure than Super Mario 64's you-need-stars-to-get-through-doors-to-get-to-Bowser-so-go-get-stars.
The gameplay is smooth, well crafted, and the whole experience feels seamless. The water effects are, naturally, somewhat dazzling, especially the sea. It's BEAUTIFUL!
Gathering the various Shine Sprites (this game's Stars) presents the usual variety of challenging battles and puzzles, along with some very interesting scenery and levels to work through. Every level is gorgeous (I cite the beach hotel at sunset as evidence), and interesting to walk around. The abilities you acquire with your squirt gun Fluud are entertaining and fun to use, and Mario has become quite the acrobat since Super Mario 64; you can have hours of fun just running around the town and jumping, spinning, and floating your way about the place.
But yes, the cutscenes, those are the important bit here. From the beginning right through to the end, the story is simple enough to follow obviously, with just hints of mystery for those who watch closely. The graphics are clean and a delight to watch. The opening cutscene, where you land on a runway only to find it covered in gunk, and the following one where you are blamed for the mess and thrown in jail, having your new companion Fluud explain the situation to you, are both smoothly done, and interesting.
What makes this game great for cutscenes though is the final boss and the scenes surrounding the leadup and resolution of that fight. It's a lot of fun, entertaining, and visually appealing. I will say two things: Anatomy is brought into serious question, and the final boss fight takes place around a bathtub.
Awesome. Undervalued game with beautiful scenery, challenging... umm, challenges, a great soundtrack, and great cut-scenes to boot. Yay.