I find it so hard to explain in words and text the feeling that I get when playing SOME games on the Wii, i've played through most (or as much as I could bare) of the games that you listed just above.
Firstly, this applies for all games, but the comfort and extra coolness of having the two 'sides' of the controller seperate is a HUGE benefit for me. Being able to itch your face (or whatever else is itchy) without taking your hand off the controller is awesome, I know that's a lame thing but I honestly feel that way.
I consider my opinion on these quite on these points quite objective for you, because I don't just think that the Wii is the be all and end all of all consoles, some of the games i've played just played like arse and I hated them while others were phenomenal and make me understand what the Wii is all about.
The first of these from your list is The Godfather
The Godfather
Now everyone I've seen so far in this thread has just pointed out 'how fun it is to bash up and punch people throw them through windows etc'. I don't want to focus on this point about the game (even though this is exactly what it feels like you are doing) I want to try and explain the concept of duel weilding with motion and button presses (it applies to DBZ too which is currently my favourite Wii game).
Think about what you can do with two hands on a controller, you've got your trigger fingers and your two thumbs for buttons on top of the controller, dual analog stick movement or dual 4 direction buttons (left right down up d pad, a b x y buttons) and two triggers.
This allows you to have a set level of moment, button presses and complexity that is set to the number of buttons that you can press with your available fingers while still feeling comfortable.
What you can do with the Wii is still have that number of buttons pressed at once, while also adding motions in to button configurations. It sounds weird but it's not, being able to walk around in Godfather while you are holding someone by grasping Z trigger on nunchuk and B trigger on Remote then swing both of them left or right to move the dude that way, then pull back one of your arms and punch.
That is one tiny little sub section of the game, doesn't even start to take into account every other different combination of movement and actions that you can do while doing other button presses, look at the things other people have said you can do and then think about what you might have to do to perform them, it's completely intuitive.
When you've got some dude grabbed from the collars, pull both of the nunchuk and remote up towards your face and your character deals a killed head butt, swing your arms to swing a dude from one side to another then let go of the triggers and they go flying like you've thrown them... it's AWESOME.
I hope that makes sense??
LOZ: Twilight Princess.
PERSONALLY I would have preferred to be able to press the A button to do normal attacks quite honestly. Shaking the remote just became exactly that after a while for me, shaking the remote to defeat baddies, I personally think this took away from some of my experience, so I was constantly Jump attacking (which is what Link does when you press A).
The REAL difference that is made in this game is the aiming with the pointer, this is truly awesome... AWESOME, if you think back to the OoT in the Gerudo Valley doing the arrow aiming task with the targets while you ride around on Epona's back, that was HARDCORE hard because it was hard to aim while you were riding with a joystick, with the remote it's still hard but if you're skillful you can aim where you want and BOOM headshot (heh).
The next big difference for this game was in the sword techniques that you earn and use during the game, the Wii Remote function of these is really awesome, jump flip attack, rolling behind an enemy and cutting him from behind, downward spike... all of these were good and used the Wii remote in combination with timing and button presses REALLY well.
Red Steel
Personally I think this game is complete arse, it's a rush job exclusive with poor controls and I don't care what anyone says about getting used to it or anything, this game sucks... I can see how FPS will work on Wii (COD3 was done right) Red Steel wasn't. Don't let playing this game set your view on the Wii.
Wii Sports
I don't know what more I can say, playing this with my girlfriend and her friends, having them want to come over for gaming and drinks nights because they want to play Wii Sports and getting my girlfriend into gaming because of this game (we don't play it that much any more) was simply awesome. Tennis is brilliant, and when you become good you can be unstoppable. Bowling is ultra fun, baseball - the bat while you are holding it (before you swing) is like 1:1 movement but when u swing u always swing along the same centre line (it's nearly impossible to hit a dipper). I don't like Golf and I like Boxing but I can never b fukd cause it's so physical.
I was going to talk about more games but simply explaining how they work isn't going to help you understand what the difference the Wii makes is... it's the fundamental difference, what I try to explain by adding an extra level of depth.
You can use joystick on nunchuk, use motion detection on nunchuk, pointer on remote and d pad on remote all for movement (like having the use of FOUR joysticks or axis of movement).
It isn't about exacting movements (though some games will do this) it's about likening the movements you make in real life to the game characters with button presses, it feels like your still playing a game but also like you have super powers... I haven't played Spiderman yet, but I want to try it out, webslinging with the remote and nunchuk movements is gonna b fuggin mad.
I'm not THAT excited about Super Mario Galaxy or Metroid Prime 3 as 'Wii' specific games, but I can't wait to see what Manhunt and any games like Godfather, Spiderman etc etc will end up turning out like.
The Wii would be the perfect console for me if it had better graphics, I want HDR lighting, I want high-res, I want all special effects and lighting (i'm a graphics whore) and this is going to be the deciding factor when I buy a lot of games, if the controls feel better and I have more fun and WANT to play more than just looking at the pretty graphics then it's Wii version for me, unfortunately RPG's generally shouldn't make use of the Wii controls or it will feel gimmicky to me, that is why I think the other consoles will be better for those type of games, HOWEVER if a company can come up with some awesome cool new battle system method using the Wii Remote for an RPG i'm ALL ears and hope it happens.
The Pointer is also very cool too, it's like having a mouse for a console game but... better.
Hope that helps, feel free to quiz me on anything :)