It's difficult to narrow almost 40 years of games down to a top 5, but here goes in no particular order!
1. Super Breakout - Atari 5200 - one of the first games that really grabbed my attention growing up, and still hasn't quite let go!
2. The Legend of Zelda: A Link to the Past - Super Nintendo - Wonderful adventure through the exciting world of Hyrule! Colorful and a very memorable soundtrack!
3. Super Metroid / Castlevania Symphony of the Night - Super Nintendo - (It's a tie, but they go so well together) Great (re)playability, story, and the relentless hunt to find everything! The reason for Metroidvanias!
4. Legacy of Kain: Soul Reaver - Playstation One - Very engaging, cinematic story through Nosgoth! This game had great voice acting, animation, mood, atmosphere, music . . .
5. Halo: Reach - Xbox 360/Xbox One - Loved the original Halo games, but this one I played for days and days and days. First game I actually worked on speed running and became fairly proficient in multiplayer!
Honorable mentions to Final Fantasy 7 - X, Tekken 3, Street Fighter 2 (all of them), Marvel Super Heroes, and Soul Calibur! Hundreds of THOUSANDS of fights!!!