I really want to post a whole horde of games, or even groups of games like "Tom Clancy games pre-2007" but I'll be strict and post the 5 games I would say define me as a gamer, i.e. what they've done for me in a respectable skill-sense and how I find such games entertaining today. They'll be in no particular order as it's hard enough just picking 5 
Unreal Tournament
Got me into multiplayer FPS and a good understanding of how multiplayer servers worked. At quite a young age it actually developed my reaction times IRL for throwing, catching, dodging tackles in sport, etc.
Rainbow Six: Rogue Spear
Taught me that you can't take anything for granted and that good planning will likely pay off. Because of it I will spend as long as I need to work on a plan, strategy, whatever. I'm not the most organised person in the word but I sure as shit plan myself out, which is always a good fallback.
Halo 3 Introduced me to competitive multiplayer. Up to that point I preferred playing bots and co-op because the only multiplayer I knew up was on PC, where I didn't take it too seriously, and splitscreen Goldeneye or Timesplitters, where it was easy to get annoyed at your friends and vice versa. Developed my social skills by communicating with strangers nicely, or plain sternly when angry. Also gave me the confidence to call out on others faults. While I will call them out, I rarely insult someone online as I like to follow the "return fire only" rule of engagement with others. My comebacks are intelligent, not derogatory, because I have a reason to argue and not to just spout crap for trash talk.
Shogun: Total War Either this or Medieval 1: Total War. Gave me an interest in long-term games where you can invest a few hours a week over many months and still enjoy it. Casual and slow strategic games. I still enjoy playing them every now and then.
The Elder Scrolls IV: Oblivion
Sucked me into western RPG's, modding, character development, lore, further reading into a subject. Most people love it, some people hate it, but I'm not afraid to say it was the first RPG to really catch my interest.
<color=black>Honourable Mentions
The Sims
Building houses and stuff. I nearly followed a path for architecture because of this game.
World of Warcraft
Captured my interest in MMO's. I also ran 2 guilds on 2 separate occasions. The second was far better than the first, but both were crap regardless. roughly 150-odd people in the second guild with 120-odd mothballed alts in it.
Splinter Cell 1-3
Stealthy, whilst requiring patience and reconnaissance.
Swat 3 & 4
SWAT is one of my favourite games because the AI is really smart and the way you analyse a situation under heat that could lead to a favourable victory or the demise of an officer is just pure gold.
MoH Underground/CoD 1/CoD 4/BF1942/BF2142/BF3
Fast-paced shooters, real-time cutscenes, large-scale battles, small cog in a big machine effect.
NFS: Hot Pursuit (Original)
Countless hours of fun with my brother on the PS1. Got me into Racing games (kind of).
Time Splitters 2/Goldeneye
Glorious split screen fun on the Xbox and N64.
That raps it up. Some really good games there. I've missed a few such as RTS's, but I didn't want to make this post any bigger than it is.
Unreal Tournament
Got me into multiplayer FPS and a good understanding of how multiplayer servers worked. At quite a young age it actually developed my reaction times IRL for throwing, catching, dodging tackles in sport, etc.
Rainbow Six: Rogue Spear
Taught me that you can't take anything for granted and that good planning will likely pay off. Because of it I will spend as long as I need to work on a plan, strategy, whatever. I'm not the most organised person in the word but I sure as shit plan myself out, which is always a good fallback.
Halo 3 Introduced me to competitive multiplayer. Up to that point I preferred playing bots and co-op because the only multiplayer I knew up was on PC, where I didn't take it too seriously, and splitscreen Goldeneye or Timesplitters, where it was easy to get annoyed at your friends and vice versa. Developed my social skills by communicating with strangers nicely, or plain sternly when angry. Also gave me the confidence to call out on others faults. While I will call them out, I rarely insult someone online as I like to follow the "return fire only" rule of engagement with others. My comebacks are intelligent, not derogatory, because I have a reason to argue and not to just spout crap for trash talk.
Shogun: Total War Either this or Medieval 1: Total War. Gave me an interest in long-term games where you can invest a few hours a week over many months and still enjoy it. Casual and slow strategic games. I still enjoy playing them every now and then.
The Elder Scrolls IV: Oblivion
Sucked me into western RPG's, modding, character development, lore, further reading into a subject. Most people love it, some people hate it, but I'm not afraid to say it was the first RPG to really catch my interest.
<color=black>Honourable Mentions
The Sims
Building houses and stuff. I nearly followed a path for architecture because of this game.
World of Warcraft
Captured my interest in MMO's. I also ran 2 guilds on 2 separate occasions. The second was far better than the first, but both were crap regardless. roughly 150-odd people in the second guild with 120-odd mothballed alts in it.
Splinter Cell 1-3
Stealthy, whilst requiring patience and reconnaissance.
Swat 3 & 4
SWAT is one of my favourite games because the AI is really smart and the way you analyse a situation under heat that could lead to a favourable victory or the demise of an officer is just pure gold.
MoH Underground/CoD 1/CoD 4/BF1942/BF2142/BF3
Fast-paced shooters, real-time cutscenes, large-scale battles, small cog in a big machine effect.
NFS: Hot Pursuit (Original)
Countless hours of fun with my brother on the PS1. Got me into Racing games (kind of).
Time Splitters 2/Goldeneye
Glorious split screen fun on the Xbox and N64.
That raps it up. Some really good games there. I've missed a few such as RTS's, but I didn't want to make this post any bigger than it is.