1. Super Mario Bros. 3
In 1989, I was the biggest 'Mario' fan on the planet. I played Mario 1 and 2 relgiously. When I learned about 'Mario 3', I couldn't wait to play it. This was before the internet, before demos, before any kind of easily accessed media. It was just a big mystery. All I knew was that it was coming, and it was going to be awesome. I give a special nomination to 'Mario World', but that was going to be on a different system that I didn't have. So the level of hype for me was not as high.
2. Sonic the Hedgehog 2
Sonic 1 was the game that turned me from a casual Sega fan into a hardcore Sega fanboy. And my anticipation for this one was as high as you can imagine. The screenshots looked hot, and the game promised to be bigger and better than the first game. And it delivered all of that and more.
3. Mega Man 9
Those who know me know that I'm a former-but-still-sometimes-bitter ex-fanboy, unwilling to change along with an industry that has changed dramatically and refused to look back. When Capcom announced that they were planning on releasing a new entry in the 'Mega Man' series, I had a rush of excitement run through my body. It was like when you were a kid and you were in the toy store and you found that ONE TOY you had to have. That's what it was like to learn that Capcom was going to not only make a new MM game, but that it was going to be a fucking NES GAME. Goosebump city.
As an aside, I never truly got 'hyped' for any of the NES Mega Mans. I discovered the series with Mega Man 2, and got hooked with Mega Man 3. I just naturally assumed that every year would bring me a new Mega Man game to play.
4. Sonic 3/Sonic & Knuckles
Sonic 2 delivered and I was in Sonic fanboy overdrive mode. I wanted more more more. I even sought out the Game Gear games to tide me over. I even plunked down 229 dollars for a Sega CD JUST for it's exclusive Sonic game. This series was my crack. It's just a pity that after 'Sonic & Knuckles', the ride was over. Never take anything for granted.
5. Mega Man 7
I loved Mega Man X, but my true passion for Mega Man came from the original series. I thought that it was long gone. When Capcom announced MM7 for the SFC, I got really excited. However, they canceled the North American release. A few short months later, they later changed those plans and decided to release the game after all. I had a reserve riding on this game for over a year, and boy was I happy when I finally walked out of the store with the elusive game in my hand. Also, Mega Man 8 receives an honorary mention here, but that game didn't deliver like MM7 did.
6. Zelda: Ocarina of Time
There was once a time when I thought the Zelda series could do no wrong. Zelda 1 and 2 were among my most favorite games ever. Zelda 3 took the series to extraordinary hights, and Zelda: Link's Adventure was just as awesome as it's SNES daddy. So, when I learned that there was to be a new ZELDA for the game-lacking N64, I was sure I would enjoy this one too. Sadly, I did not really enjoy the game, and have been down on the series ever since as each subsequent Zelda game has been in the same vein.
7. Punch-Out!! Wii
Like Mega Man 9, this was one of those games that I wanted for a long, long, LONG time. When Nintendo quietly announced this game, I was a little excited, but also a little skeptical. Nintendo has changed every one of their series to the point where I don't enjoy them much anymore. What would they do to Punch-Out!!? Well....they didn't do a thing! Except make it better! It blows the NES and SNES versions out of the water. It's one of those rare games that lives up to AND exceeds the hype.
8. Sonic X-Treme 
I purchased my Sega Saturn the day it came out in early 1995, KNOWING that there was going to be Sonic games released for it. After all, there had been numerous Sonic games available for the Genesis, Sega CD, Game Gear, and even the 32X, right? Sega would be stupid not to release a Sonic game for their next system. Well, as I later learned Sega originally had absolutely no intention of releasing a new Sonic game for their vaunted Saturn platform. The company felt that they didn't want to be known as the 'Sonic' company and wanted consumers to concentrate on their other games. When they later realized this error, they quickly scrambled to put together a new Sonic game, without the involvement of Sonic Team, who had 'retired' from making Sonic games(at that time). I didn't care, I just wanted a new Sonic game. I knew it was going to be good. Why wouldn't it? Every Sonic game beforehand had been great! And this is a NEWER system. Better technology means better games, after all! ( < How ignorant I was) Later, the game was cancelled, and the only game that the Saturn ever received was 'Sonic 3D Blast', a game that I did not enjoy. Eventually 'Sonic Adventure' was announced for Sega's next system in 1998. I was excited, naturally. But by that time, I wasn't sure if Sega still had the magic touch. They didn't.
In the end, I enjoyed my Sega Saturn a great deal despite the lack of an original Sonic game, and it remains one of my most played/loved systems I've ever owned.
9. Super Mario 64
Holy shit, MARIO'S BACK???
AND IN 3D???
YES!! I must buy this N64!!!
In retrospect, though, it's a pretty boring game to play nowadays. But come on, it was the FIRST truly 3D platformer. The magic of playing it for the first time cannot be duplicated.
10. Nights: Into Dreams
GameFan magazine got me onto this one. The level of hype they thrust upon it was like no other. The game looked absolutely beautiful. I was told that the graphics were the best available for the Saturn system, and had great gameplay to back it up. This one didn't disappoint, and remains one of my favorite games of the 32/64-bit era.