Continuing the topic from earlier:

http://en.wikipedia.org/wiki/Category:1991_video_games

Here's my top 10 in no order:

1. Tiny Toon Adventures
2. Sonic the Hedgehog
3. Teenage Mutant Ninja Turtles: Turtles in Time
4. Battletoads
5. Adventure Island II
6. Lemmings
7. The Legend of Zelda: A Link to the Past
8. M.C. Kids
9. Megaman 4
10. Street Fighter II

Notes: This is a really tough year!

I also had to struggle to find 10 games I played from that year. Not in a specific order (actually there are more or less in order of preference. (Sort of,I didn't have a Genesis, but managed to play the last 2 games briefly)

M.C. Kids
Street Fighter II
The Simpson (Arcade)
Legend of Zelda: A link to the past
Final Fantasy IV
Tiny Toons Adventures
The little mermaid
Super Ninja Boy
Streets of Rage
Sonic the hedgehog

1. Sunset Riders
2. Zelda: LTTP
3. TMNT 4
4. Final Fantasy Adventure
5. Lemmings
6. Street Fighter 2
7. Final Fantasy Legend 3
8. Lagoon
9. Mega Man 1 gameboy
10. Spanky's Quest

1.Zelda: A Link to the Past
2.Final Fantasy 4
3.Sonic the Hedgehog
4.TMNT: Turtles in Time
5.Megaman 4
6.Megaman 1 (GB)
7.Captain America and the Avengers
8.Chuck Rock
9.Jacki Chan's Action Kung Fu
10.adventures of Lolo 3

10. Street Fighter II
9. Street Fighter II
8. Street Fighter II
7. Street Fighter II
6. Street Fighter II
5. Street Fighter II
4. Street Fighter II
3. Street Fighter II
2. Street Fighter II
1. Street Fighter II

I decided to take this list differently than my last list, as it's unlikely that there will be any yearly list where I've played more than ten games.

Favorite of the Year:
Final Fantasy IV

Other Games I played and liked:
Final Fantasy Legend III
Joe & Mac
The Legend of Zelda: A Link to the Past
Sonic the Hedgehog (Genesis/Mega Drive)
Super Bases Loaded
Super Castlevania IV
Yoshi

Played but didn't like:
Metroid II: Return of Samus
Star Wars (I had the Game Boy Version)

Though I'm apparantly closer to toppling ten than I thought. It's kinda sad, actually. I don't get near this many games yearly now that I'm grown up.

You don't have to own them to experience them. It could have been at a friends house, rental, or borrowed... I think as long as you've played enough of the game to make a judgement, then you should be able to list it.

Oh, I know. Both Final Fantasy IV and Joe & Mac were rentals for me. Or else this list would be even shorter.