"Games that Define Us" Topic

Its kind of an interesting topic when you sit down and think about it a bit. They don't make us who we are but they certainly have an influence of one kind or another. I saw this first at Dulce et Decorum. He was able to keep it to ten, I had to go to twelve. You can see the list that got me started with this here:
link
Edit: apparently the concept was first introduced here: thefrontlinegamer.blogspot.com
This is my list:
1. Gettysburg, AH 1965 Edition
2. Dungeons & Dragons, TSR 1976 White Box
3. Squad Leader, AH 1977
4. Traveller, GDW 1977
5. Tractics, TSR 1975
6. Fire & Steel/System 7, GDW
7. Empire Builder, Mayfair Games 1980
8. Civilization, Francis Tresham
9. Johnny Reb, Adventure Games (John Hill)
10. 1830, AH
11. Napoleon's Battles, AH
12. Fire and Fury, Rich Hasenauer

Again, I'm not saying that these are the greatest games of all time or anything, just the ones that shaped my life experiences in some way or another.
If you want to see why visit my blog at link

What's your list look like?

For me it was Palladium's Recon rpg with the minis game in the middle of the rules and Warhammer 40,000 Rogue Trader.
Edit: and Battletech.

1. Tactics II
2. Afrika Corps
3. Dungeons and Dragons AD&D
4. Squad Leader
5. Terrible Swift Sword
6. Flat Top
7. Marine 2002
8. Star Frontiers
9. A Gleam of Bayonets
10. Chess

I formed a lot of friendships around these games.

In no particular order:

1) Rally Round the Flag (orignal 70's ACW version)- First set of minis rules.
2) Avalon Hill's Russian Campaign- Was my first exposure to, and sparked my interest in, the WWII Russian Front
3) Avalon Hill's Squad Leader- Taught me lots about WWII and small unit warfare.
4) D&D- First RPG
5) TSATF- First exposure to Colonial gaming and individually mounted figures organized in units.
6) Angriff!- First WWII miniatures rules
7) Deadlands- The minis inspired my interest in VSF
8) Empire- Taught me that ultra-detail, didn't equal ultra-fun
9) Blood & Swash/Thunder & Plunder – First published set of rules
10) Charge!- Showed me that going back to wargaming's roots, still had something to offer.

Panzer Leader
Starship Troopers
SPIs Air War
D&D White Box
Chainmail
Gamma World
Traveler
Stars And Bars
WRG 5th-7th
DBM
Seapower
That's 10 off the top of my head.

Hmmm, tough one. As you said, hard to keep the count down. Let's see, in no particular order:

1) Starfire, TFG
2) Ogre/GEV, Metagaming. I suppose that's really two games, but I actually got GEV first and Ogre has always felt more like a specialized scenario than a standalone game to me.
3) Amoeba Wars, AH. No, really. Fond childhood memories.
4) Gamma World, TSR.
5) SuperSystem, Four-Color Figures.
6) Cosmic Encounters, Eon.
7) Runequest, 2nd ed, Chaosium.
8) Legions of the Petal Throne, TSR. My introduction to Tekumel.
9) Rogue Trader, GW.
10) Full Thrust, GZG.

Chief there are some good ones on that list, a couple that I had to dwell on before picking something else; Ogre/GEV, Amoeba Wars (totally with you on this one) and Cosmic Encounters could all of been on my list.

1. Dungeons and Dragons. This blew my 12 year old mind in 1980.
2. Chess. Been playing since sixth grade (ironically about the same time I took up D&D).
3. SPI Soldiers. First true wargame I ever played. Saw it at Kaybee toys for $2 USD on sale. Fun introduction to chit wargames and created the bug in me for true wargames.
4. Knight's Hand. This is a regional bit of rules that were sold at GenCon back around 1983 or 1984. It's straight up simple bit of skirmish rules. They aren't great, but these are the rules that got me completely into miniatures. I still have the rules, but haven't found another sole out there who has ever heard of them.
5. Battle Cry- Not the version from Avalon Hill or the 150th anniversary version from Avalon Hill (I have both), but the original 1961 version from Milton Bradley. I found this game at the local library as a 7 year old in the mid 70s and it started the whole trend that would take over my free time for life (and I eventually bought this version as well, completing my trifecta).
6. Attack of the Mutants- Yaquinto Games. They gave away this game for free to anyone who wrote them a letter when I was in middle school. You better believe I did. It was awesome. I bought nearly their whole library after that- (and they weren't as awesome).
7. 1941 GDW- The entire Russian Campaign in 120 minutes? I played the crap out of it in high school.
8. PanzerBlitz- Avalon Hill- A friend of mine had this and it was an eyeopener for me.
9. OGRE- I was poor, it was $5 USD and incredible. I still play this game, have the miniatures and was on the kickstarter day 1.
10. Twilight 2000. As much as D&D opened my eyes and made for a lifetime of fun, Twilight 2000 made my high school years. I still have nightmares about the time we rushed a T-80 in a Bradley. We were stupid. We didn't know any better. We died. (And then the GM told us that the T-80 was looking to join us and we just opened fire. We were REALLY dumb).

That's just 10. I could name 100.

Chainmail
Tractics
Fletcher Pratt Naval Rules
AH games(all)
SPI games(all)
Traveller
Europa game series
Rogue Trader
La Battaile de la Moskowa
Star Fleet Battles
Blue Max
GURPS
….and on and on….

TWISTER!!

1) Tactics II – first wargame and couldn't find anyone who would play it with me in high school because it was so complicated!
2) Gettysburg 1965 AH edition – probably my most played wargame in college
3) France 1940 SPI – first encounter with a wargame with a mechanized movement phase
4) Blitzkrieg – well remember a weekend long game I played in college – first one that I had dreams about
5) Chainmail – first real miniatures game was played using these rules
6) Napoleon at Waterloo SPI – likely my most played game – started with the first version where the French had a hard time losing, then SPI stuck that British 1-4 unit in Hugomont and the game outcome was a different story!
7) Mech War '77 SPI – I still think of this as "modern"
8) Terrible Swift Sword – eventually developed a miniatures version which let to a lifetime of modifying game rules to suit my perspective (which has changed with time and more detailed historical reading)
9) WRG Ancients 5th Edition – played in one tournament and swore off ancients for nearly two decades – a wargaming buddy once deemed these "the ideal rules for engineers" – since I was an engineer, I wasn't offended
10) North Cape by CinC – my intro to using miniatures on a hex board plus introduced me to General Quarters I & II and that naval wargaming was not just about spending 30 minutes rolling dice and looking up various charts to determine my single hit took out a searchlight

In no particular order:

Charles Grants 'Battle'
WRG 16xx – 18xx
WRG 1925-50
Panzerblitz (AHGC)
Squad Leader (AHGC)
Third Reich (AHGC)
Hells Highway (VG)
D&D

and more recently

DBA
AK47
Square Bashing
Lost Battles
Spearhead

Interesting topic. Mine in rough chronological order:

5th Ed ancient rules (WRG) – started me in miniature games, although 6th put me off for 14 years.
Tractics (TSR) – started the whole WW2 20mm thing
Traveller (GDW) – it got me RPGing and about the only RPF I really enjoy.
Empire of the Middle Ages (SPI) – this defines my multi-night multi player boardgaming. I played quite a few campaigns and still would play again
Civilisation (AH) – this is the all day multi-player boardgaming. Played it lots. Still great.
Family Business (Mayfair) – my favourite filler game.
DBM – got me back into playing ancients in 1994. Only game I played a tournament with.
WarpWar – love this little diceless game and helped work of additional rules in the early days on the web.
Armati – made me realise there were more rules than WRG out there and played nothing else for a long time.
Take Cover!! (Britannia Miniatures) – got me back into WW2 after 10 years and still really only play these rules.
Warrior Kings (now Rally Round the King) – showed me a completely different paradigm for ancient gaming. Still like this lots, along with Armati.

Dungeons & Dragons
Call of Cthulhu
Battletech
Warhammer 40k
Necromunda
Battlefleet Gothic
Gaslight
The Sword and the Flame
Mausoleum
Wagers of Sin

For me..

Charles Grant – Battle
Airfix Guides – Various (not a game, I know..)
Chandler's Napoleons Battles
Decline & Fall (Boardgame)
Waterloo Quad (SPI)
Newbury Napoleonics
D&D (1st Edition)
Call of Cthulhu (1st Edition)
Traveller
Cold War Commander
Langtons Signal Close Action (FastPlay)
Full Thrust
Polemos ECW
DBA
DBMM

Hmmmmm too many, but all (for me), seminal.

Charles Grant – Battle
Afrika Korps
Chain Mail
On to Richmond
Fire & Fury
On to Richmond
WarHammer Ancients
Black Powder

Risk
AH Gettysburg
AH Panzer Leader
AH Squad Leader
Stargrunt II
VOR
VOID
Necromunda

TWISTER!!

If we're going to count mating rituals as games, put Beer Pong on my list. :)

Rough chronological order

Checkers (learned from great uncle born c. 1895 about giving best effort)
Plastic Cowboys & Indians (basically what I do today w/ miniatures)
Poker (Dad taught me. We played socially.)
Chess
Homebrew Baseball card Simulation (one of my first designs)
D&D
BattleTech
Tonk (serious game with heavy wagers)
LOTR SBG
Commands & Colors Ancients

Chess
Jutland
Fletcher Pratt
Seapower
Chainmail
Tractics (in a negative reinforcement way)
Traveler
Warhammer
40K
Force on Force

Charge!, WRG Ancients 3rd edition and WRG microarmor rules defined my expectations for miniatures games. Not so much the mechanisms as how I interacted with the game.

A long-running campaign of the Renaissance set my (high) expectations of a campaign game.

Traveller defined my expectations in an RPG.

As long as we're tripping down memory lane, here is my list. There are a number of other good choices, such as Tactics II, Traveller, and Squad Leader, that others have mentioned. Getting the list down to 10 is hard.

1 – Little Wars: After reading about wargaming in appendix at the back of The War Game by Charles Grant, I discovered the late '70's reprint of Little Wars, cut out hills, made buildings, and collected up the various Britains firing cannons like in the book. I had hours of fun on the back patio with tolerant friends.
2 – Cemetary Hill: This was one of the SPI folio games. My grandmother bought it and Antietem for me, thinking they were books. The rest is history.
3 – Dungeons and Dragons (in the blue box). This was my first role playing game; although, we quickly converted to Tunnels and Trolls, which I still like better.
4 – Firefight: SPI game about "modern" combat in Europe. As someone who was thinking about the Army as a career, this was a formative game for me.
5 – Rally 'Round the Flag: This was the first set of miniatures rules I bought. I still think it is a fine set of ACW regimental-level rules. I cut my teeth on painting hordes of Airfix ACW figures for these rules.
6 – Empire III: My first set of Napoleonic rules. We played the hell out of these rules when I was a cadet. Complicated, yes. They don't suit my tastes today, but we had loads of fun with them in the days when complicated equalled good. They sparked a lifelong interest in the period. (I actually liked Empire II better.)
7 – Fury in the West: This was a game of the battle of Shiloh. I really found the way they explicitly represented stragglers innovative. Many years later, I drew inspiration from this game when I was designing Santa Anna Rules.
8 – Napoleon: This was the original "blocks" game. This game is truly elegant. I think it might be the best board wargame ever invented. Subsequent revisions have NOT improved this game. The original version had a battle map that elegently simulated army commander-level decisions. The blocks and the campaing map were an elegent mechanism for strategic maneuver. This is the game I wish I had invented.
9 – Wooden Ships and Iron Men: Actually I played Ship of the Line, the miniatures version, and really, really enjoyed it. This is still a great game.
10 – Panzer, 88, and Armor by Yaquinto.
11 – Look, Sarge, No Charts: World War II: This is set of rules I wrote, but this is not meant to be a plug for them. I've published a number of sets of rules over the years, but this one, though largely overlooked by the hobby, is the one of which I am most proud.

Buck Surdu

Difficult to narrow down! Keeping only to the ones that have had the most influence and/or long lasting appeal here is my list:

Broadside & Battle Cry from Milton Bradly (earliest)
Third Reich, AH (1st and probably most played board game)
Panzer Leader/Panzer Blitz, AH (2nd most played board game)
War and Peace, AH
Starship Troopers (AH original version)
SPI's Great Battles of the American Civil War series
ICE's MERP/Rolemaster RPG (still playing this one)
Traveller RPG & 5th Frontier War from GDW
Empire III, Empire Games Inc. (1st miniature rules, difficult but enjoyable)
On to Richmond, by Paul Koch (elegantly simple)
The Sword and the Flame by Larry Brom, 1st revision (an instant classic)
WRG Ancients 6th edition (after Empire, not as hard as it looked)
Donald Featherstone's Skirmish Wargaming (taught me how to fight small battles)

And that just gets us into the 80s!

Scrabble (with my mom)
Monopoly
D&D
other games I stole from when I ran D&D (ie Bushido, Gamma World, Metamorphosis Alpha)
Champions
Fantasy Trip

on and on

Grant's Battle.
Warhammer 40K Rogue Trader.
DBA.
Memoir '44
Command & Colours: Ancients
Songs of Blades and Heroes
Settlers of Catan