Super Monkey Ball is a hard-core action game designed in a very old-school style, with a very long and fairly steep (especially near the end) learning curve.
For those of you who have played Marble Madness, this is essentially a modern remake, with monkeys inserted into the marbles for added pathos. For those who haven't, a good comparison would be the tilting board Labyrinth games you played at your Grandmother's house, in which you guide a ball bearing through a maze.
For those who haven't played either, and I guess for clarification for those who have, your objective is to guide a monkey in a sphere through 100+ obstacle course levels, without too often letting time run out or falling onto any of six well-rendered landscapes several thousand feet below.
The emphasis is very clearly on action gameplay. It's not an exploration or puzzle game. There is no story, and no attempt at creating a realistic setting. Like the arcade games of the early 80s, the focus is on optimizing your play style over the same material to be rewarded with a high score, and occasionally more levels to play.
The more-levels system works like this: finish any of the main three modes without dying, and you open up the extra levels for that mode. Beginner mode has 10 regular levels and 3 extra levels, advanced mode 30 and 5, and expert mode 50 and 10. Reaching the extra levels in expert mode is a superhuman feat, and ... if you beat the 50+10 levels without using a continue (3 lives + any extra lives you earn), you open up another set of even more difficult levels, which in all probability have not been beta tested very well.
So there's a lot of game here to keep you busy. However, once you factor in the price of replacing broken controllers, it's a tossup as to whether it will end up being a good value; The frustration level is very, very high. A lot of this is due to the insanity of the level design (take a look at some of the movies at http://www.mple2k.com/smb/index.html for examples of the more guilty), but quite a lot is also due to the horrible camera. The camera is far, far worse than any i've seen in any (other?) 3d platformer, and you are given no direct control over it whatsoever.
The physics implementation is excellent. You bounce off of corners and tilted (and curved) surfaces realistically. Friction is fairly low, so you have to take acceleration and deceleration into consideration, and also moving platforms will have the tendency to slip out from underneath you if you're not already moving at their velocity. Staying on rotating platforms can be difficult as inertia (or centrifugal force, if you prefer) pushes you away from the center.
The literature claims that you don't have direct control of the monkey, but instead you tilt the game board. You do clearly tilt the game board, but you have control of the monkey in the air as well, so it seems to me that the board tilting is a gimmick that should've been done away with. With the onscreen tilting of the board and the swirliness of the camera movement, being able to tell what's going on is sometimes very difficult (again, see the gameplay movies located at the URL above).
Graphics? Enh. Not the point. The game runs at 60hz. The backgrounds are nice looking. The playfields are functional. Mirroring and shadowing effects abound. The monkeys are pretty strange-looking. Cute, sort of. Oh, and the desert levels simulate refraction of hot air currents. I haven't seen that one before.
Of multiplayer modes, you have seven: you can play the main game to see who finishes each level first. Monkey Race, which has six courses designed specifically for multiplayer racing. Monkey Fight, which adds a boxing glove on a spring to each monkey sphere. Monkey Target, in which you jump off a ramp and split the ball apart to form "wings", to attempt to hit targets floating in the ocean. I've heard the last part compared to Pilotwings.
Monkey Billiards and Monkey Bowling are the best simulations of billiards and bowling I've ever seen, although the last time I sampled either genre was in the mid 80s. Monkey Golf is a fun miniature golf game, though some of the holes seem to be just random luck (get a hole-in-one or die).
Target, Billiards, Bowling, and Golf are all playable with up to four players even if you only have one controller. The other modes have simultaneous play, so require one controller per player. It's a good party game, but it's probably not worth buying solely for that purpose; if that's what you're looking for, wait for Super Smash Bros Melee.
But if you're looking for a hard-core remake of Marble Madness designed in a very old-school style, with rewards in the form of extra levels scattered along a very long and fairly steep (especially near the end) learning curve, this is what you're looking for.