In no particular order:
1) Pac-Man Championship Edition DX+ (PS3, also XBOX360 and Steam) I personally think this is one of the greatest video games made in the last decade. A follow-up to 2007's
Pac-Man Championship Edition, the two are often confused.
DX was released in 2010 and took the Pac-Man of the 80s arcades and turned it into a game for the modern crowd: fast-paced, visually stimulating, online leaderboards, endless replay value. An update with new levels was released last year and the game was re-branded with the "+".
2) Shadow of the Colossus (PS2) Much like
Journey for PS3, this game is largely about the overall experience. Some games are all about hardcore skill
, while others are about immersing yourself in another world. SotC is a beautiful game with great music, but it's not without its challenges. Defeating Gaius' Hard Time Attack is one of the most frustrating and rewarding things I've ever done in gaming.
3) Sonic the Hedgehog (Genesis)A classic that needs no introduction. While Genesis franchises generally play 2nd fiddle to Nintendo franchises in popularity and critical acclaim the early Sonic games were masterpieces in level-design and music. Someday I will be making speed/score runs on this title.
4) Lightening Force: Quest for the Darkstar (Genesis)Yes, "Lightening" with an "e". This game is part of the
Thunder Force series but was renamed for NA consumers. I'm generally horrible at shoot 'em ups, whether they be vertical or horizontal, but I have a love for this game that stretches back to the days when renting games from the video store was a special occasion. I remember figuring out one of the cheat codes on my own and this allowed me to play all the way to end of the game. As a result, this was the first game I truly tried to break down and learn. It's not without its faults (serious leeching opportunities and massive slowdowns), but the music is probably the best-produced of any Genesis game. The programmers really pulled everything out of the sound chips with this one.
5) Final Fantasy VIII, X, XII (PS1, PS2)Picking three Final Fantasy games is cheating for a "top 5" list, but I couldn't narrow it down from these titles. I could write pages on each of these three games, so I'll be as brief as possible:
VIII: Pure nostalgia and great music make up for the broken "Junction" system and relatively uninteresting story.
X: A spiritual story that I feel can reach most people who pay attention, as opposed to so many RPGs that involve an arbitrary "oh no our kingdom is being attacked!" storyline.
XII: AMAZING music and a fresh battle system. If you like to grind and love super-bosses with tens of millions of HP, this one is for you.
Honorable Mentions: Penguin Land (SMS) and all the games Katie mentioned 
Penguin Land is a relatively unknown puzzle platformer for the Master System. Not terribly difficult and once you know the route the only replay value is in doing it faster. The coolest thing about this game is that there is a level creator and that blew my mind when I was a wee lad.
