Narrowing down to 5 is a tough one for me, and for lists like these I always write a number of reasons for my choice, so be prepared for rungs of text. With that said here are my favourites in no order :
1. LoZ Wind Waker (GameCube)
I was tied between Wind Waker, Twilight Princess and Ocarina of Time. But I chose Wind Waker in the end simply because I think it's the better game overall. OoT was a huge success because of it's gameplay style and how easy it was to just pick up and play and also because of the massive open world and great story.
TP grabbed people's attention because of the realism look, it also had a great story to go with it, and because it was a Wii launch title. Wind Waker meanwhile took everything great from OoT and basically changed the story around a bit. I think one thing that turned most people off was the cel-shaded approach Nintendo took. It was a risky move and really split the fans of the series (suprisingly no boycott insued), but I think it was the right move. While some people hate the look, I thought it was great. But I will concede the boat travel was bloody boring sometimes.
2. Super Smash Bros Brawl (Wii)
What hasn't been said about this already? When this was announced, I went and pre-ordered straight away. Admittedly it did dissapoint a little bit, the story seemed tacked on and was only there so you could unlock all the characters. But the Smash series has always been about the multiplayer and it doesn't dissapoint, especially with online support (albeit some which had intolerable lag). I've heard some people complain that the Smash Ball makes the game extremely unbalanced, which is true in online play against random people. Also my main characters are MetaKnight, King DeDeDe and Jigglypuff. One more thing that was included in this game, who would win in a fight between Mario and Sonic? A question that had been asked repeatedly for over a decade, finally answered.
3. Super Mario All Stars (SNES)
It's great that Nintendo put 5 of some of my favourite games into one cart. I'm so grateful. Especially with the inclusion of the Lost Levels, which is unquestionably one of the hardest games I've ever played but fun nonetheless. I have still never finished the original SMB, it's on my to-do list. Doki Doki Panic is still fun to play and it taught me that you can vanquish monsters by throwing veggies at them. Fear my turnip of smiting! SMB3, which some fans consider to be the best Mario game ever made (I don't think that personally) is pretty cool, but damn is the last world hard. Finally there is Super Mario World which introduced Yoshi to us all. SMW is massive and has something like 96 levels, I've only found 92 at the moment but I will find them all someday.
4. Kirby Super Star (SNES)
Again another compilation cart, but I love this game. Sure the Kirby games are easy, but thats why I like them. And also, you can EAT your enemies then steal their powers, my favourites being the Hammer and the Chef. Plus you are constantly unlocking new games like Great Cave Offensive, Revenge of MetaKnight and Milky Way Wishes. It also has co-op mode in every game which is cool, although everyone I play the game with sucks at it.
5. I can't think of another one. Seriously. There are loads of games that I would defend to the death, but I can't choose just one to put here. If you read all that, you should get a medal. I'll send it in the post.