The lowdown:
The original Trauma Center is already one of the most original and fun games on the Nintendo DS but although this is largely just a remake of that game it's more than welcome on the Wii. As accurate a simulation of real medicine as Phoenix Wright is of law (i.e. not very much) you'll nevertheless have great fun repairing hapless patients with ailments that start of as simple tumours to bizarre fights against evil terrorist nanobots. What really makes the game though is the simple intuitiveness of the controls, with the precise movement of your scalpel being one of the best endorsements of the Wii Remote's accuracy. The game's no push over though and you'll need to employ the mysterious bullet time style "healing touch" to make sure you don't end up the Doctor Death of Hope Hospital.

Most exciting moment:
Although the game is a remake of the DS it does include several new missions, an extra playable character, new operation types and new surgical tools - including a defibrillator which demands a shout of "clear!" every time you use it.

Since you ask:
A surgery game was one of the first styles of games hinted at in an introductory video for the Wii, which also showed people appearing to play games involving fishing, cooking and playing the drums - amongst other non-typical games concepts.