With that out-of-the-way:
An honorary #11: Minecraft.
Minecraft was the game that brought me to the show, so-to-speak. I was always a fan of legos, but I always wished I had more. A digital version of legos, where I have infinite legos? Awesome. Minecraft is one of those games that puts itself in front of you and declares you should entertain yourself. It doesn't really have a story (and the one it does is just much to much effort to get to). You make our own story, but eventually you run out of things to do. I've found diamond. I've built a 20-story castle, a treehouse, my actual house, giant statues of Minecraft characters, a full-sized-version of H.H. Holmes' Murder castle... what do I do now?
But there are some reasons it didn't make the list. Largely, I've picked cerebral games for this list. Games with great stories that make you think and, as I've said, Minecraft doesn't really have one. And the monsters, while beloved, are a baffling choice. Before the inclusion of the starter chest (and in some cases even after) it's quite unclear what you should be doing, and I always have the wiki open.
But I can't deny Minecraft deserves a place in gaming history, perhaps more than some of the other games on this list, for being a truly innovative video game that is always trying to improve itself. Maybe someday I'll be able to survive 10 minutes in The Nether.
10: Fallout 3
AND
Fallout New Vegas GOTY
These games make the list for largely different reasons, and I find it hard to pick a favorite between them. I often find myself confusing them for the same game, mentally merging plotlines, characters, and locations. Indeed, it's often been said that NV feels like a DLC of Fallout 3. But, while they are clearly both of the same universe, they are two very distinct games.
In both games I quite appreciate the customizable character. While Yahtzee of Zero Punctuation, in Extra Punctuation, claimed the multiple dialogue options took him out of his immersion and gave him pre-determined character sets, I quite enjoyed them. I never found a point where I thought my character simply wouldn't say that.
The basic idea of the Cold War escalating is very well thought out, and the world of the vaults is fascinating. I was always disappointed when I reached the edge of the games purely because I ran out of places to explore.
Fallout 3 has a great environment. Washington D.C., as one of the harder-hit places and the base of what remains of the U.S. Government, has a lot of really interesting things to explore. It feels incredibly apocalyptic as it has barely recovered from the war. The plot of Fallout 3 is one of the best gaming plots I've ever seen. I knew of the death prior to playing the game, but I managed to convince myself he didn't die because I loved him that much. No other story has managed to make me so devoted to a character.
Fallout 3 falls flat in some very important areas: it isn't big enough. This probably wouldn't have been a complaint if I played these games chronologically, and it would be straight-up unfair to compare it to Skyrim, but even putting it next to New Vegas makes it feel tiny. It's very difficult to avoid the plot without accidentally wandering back into it. And again, this isn't necessarily a bad thing, but it really hurts replay value.
The moral choice aspect. Fallout 3 had some good parts, which Bethesda would clearly develop later in New Vegas. But it was often very difficult to pick the "bad" choice, especially in the two biggest options:
Blow up Megaton, or don't?
Poison nearly everyone, or purify the water?
Blowing up Megaton gets the player a better house (if mods aren't involved), but it's incredibly hard to justify to yourself blowing up a town (with good quests, collectibles, and one of the better merchants) just for a house.
The final decision, purify or poison, had more weight in the original game (without DLCs.) As the player had to choose between killing off every creature with radiation-induced-mutated-genes (also known as anyone born outside a vault) to get rid of the Super Mutants and Ghouls, and give humanity a fresh start, or finish your father's goal and purify the lake. When the player was set to die at the end the player didn't have to consider themselves as part of it, as they were born outside of a vault. It was essentially shooting themselves in the foot. Why do it?
Finally Fallout 3 had some DLC issues. I disliked The Pitt for the same reason I disliked the main game: the choices didn't feel right. I ended up killing all the slavers but refusing to kidnap the baby. I had to try to survive fighting my way out while killing as few slaves as possible, as refusing to kidnap the baby (thus leaving it with the people most likely to be able to get the cure out of it) was treasonous. (But to be fair, to get to that point I had to kill their leader.)
I felt the space DLC didn't go far enough into the setting. Why was killing some aliens okay and others not? What the hell just happened? I was expecting, at the end, for an alien to come in speaking perfect English (due to some translation thing) and chew the player out for killing all the other aliens, but nope. It was merely too simple.
Operation Anchorage is almost unfinishable (also known as "I couldn't finish it.")
If I could pick and choose Fallout 3 DLCS (which I can't, as I got the GOTY edition with all included) I would have only gotten Broken Steel and Point Lookout. Point Lookout was pure fun. The most interesting part being when the player could pretend to be a Chinese spy from before the war, and see a bit from their side. (It isn't pretty.) Broken Steel had some good emotional depth, and is required if the player wants to play the game past the end, but it does raise one huge question: how on earth did the player survive when the father died? (I prefer to think the father is a ghoul now, and that's why his body is absent when the player returns at the end.)
New Vegas fixed a lot of the issues with Fallout 3. The end game is significantly more dynamic and interesting, with several options to choose from rather than just "good" and "evil." (Though they do create a path that is incredibly hard to agree with following, the slaver Legion.) There's evil, then there's three shades of gray. (House, NCR, and Independent.) Rather than a full-on morality system New Vegas runs on a reputation system, which felt much more realistic. The environment is significantly bigger, which gives it better replay value than 3.
New Vegas' DLCs are significantly better. I would even argue they are almost required for the game (hence the GOTY suggestion, since you can get the game independently.) Old World Blues, Lonesome Road, and Dead Money were good enough to be their own games. All the DLCs had references within each-other or the main game. (The courier that turned down your job, Big MT being mentioned once or twice, and the burned man.)
New Vegas still has the worse story. It falls flat-on-it's-face, but does manage to get back up and finish strong. As it has been frequently pointed out: why should the player hunt down the person who shot them in the face? Shouldn't that be a life lesson not to mess with that person?
Either way, both games deserve to be in any player's library, and I eagerly await Fallout 4. (It is important to note that Fallout 3 is now quite difficult to get running on PC, and shouldn't be bought without some careful consideration. I have been able to make it work, as have many others. It just takes more effort than some people might want.)
9: Half Life 1
This is the oldest game on the list. I'm not an FPS person, so an FPS has to bring something special to the table for me to like it. And even though I dislike the silent protagonist (even though it shows up in seven of my top games) I do feel an affinity for Gordon Freeman. There's not too much that can be said of Half Life 1 that hasn't already been said, except that a full remake, supported by Valve, has been released. It's called Black Mesa. Any weaknesses the original game had are plugged, from graphics to AI to the scientists getting gender balanced, to the soldiers having more personality than "hang on a second why are you shooting at me?" And it's free. So go check that one out.
8: Antichamber
Now here's a game you probably haven't heard of. Antichamber is considered an 'anti-puzzle game.' It's a philosophical little thing that really has to be experienced for itself. Each room has little pictures that, when clicked, give the player a little saying. There's rooms where the player has to walk, rather than run, to progress. Ones where the player has to take a leap of faith. And ones where the player must see if the grass is truly greener on the other side.
This one is rather plot-free. No characters. No voices. It's a think-piece, and a beautifully done one.
7: Portal 2
A lot of people would probably expect I would have put Portal 1 on the list rather than 2, and to be honest, while Portal 1 is a neat little game, I genuinely prefer Portal 2. It is the epitome of the organic plot, with the player discovering the rise and fall of Aperture as they delve into the facility. It's also quite funny, and longer than Portal 1, which is a plus in my mind as I wanted more Portal 1.
Plus Portal 2 finally gave Chell what she wanted most, and I felt incredibly happy for her. Even if it means we don't get a Portal 3. (Though imagine an FPS where Chell uses the portal gun to kill people. It would be kinda awesome.)
6: Batman Arkham Asylum
If I were writing this list two years in the future I suspect I would have put Arkham Origins on the list, as I enjoyed it quite a lot despite the bugs. But the fact is, it's 2014, Arkham Origins is still a buggy mess, and Arkham Asylum is still the most tightly-plotted most-fun game of the Arkham series.
Asylum was my introduction to Batman and it made me a big fan. I liked The Joker, especially once he got control of the P.A. I liked finding the riddles. I liked taking mooks down one-by-one as they began to realize I was present, they couldn't see me, and I was taking them down.
The Arkham series likes to ask questions--and then try to answer them--about the Batman series. They're always quite heavy-handed about their answers (Batman actually switching places with the Joker at one point, the Joker pointing out if Batman had just killed him less people would have died) but they aspire to be smart, and that should be rewarded.
5: The Elder Scrolls V: Skyrim
OF course this game would make it on this list. Skyrim not making it on this list would be indicative of only one thing: I hadn't played it. Skyrim takes the customization of Fallout and takes it up a notch, allowing the player diverse styles of play, several hundred hours of fun, and a wide cast of characters that can truly be cared about.
I did eventually have some issues with Skyrim, centering in Whiterun (why is it the Companions will have never heard of the player even after they slay a freaking dragon in the town?) and around the Forsworn, but they're minor and petty problems that only got in the way of my experience after 700 hours of play.
4: Assassin's Creed 2:
I was not expecting much when I got this game. I heard something about how popular it was, and how you could jump around on rooftops and sneak up on people and kill them. What fun, I mused to myself. This game surprised me 10x over with the complexity and depth of its plot. It's another game that hardly needs explaining.
3: Dishonored
Dishonored, once again, surprised me. I bought an assassination game, and I got an incredibly interesting, complex sneaking game. With the Outsider, the powers, the Everyman of the Abbey, the in-game-text, the twist I did not see coming, and the simple fact that the player is encouraged to outsmart the AI (and it's difficult to) makes this one of the best games I've ever played.
2: The Stanley Parable
Another indie game related to Valve with another silent protagonist, The Stanley Parable is a game that truly explores choices in the medium of gaming. (And it's hilarious.) Essentially, you are Stanley, a man who realizes everyone in his office has disappeared. He is being narrated by a british man, who tells the player what to do as if they have already done it.
The player doesn't have to do it. The choices range from completely ignoring the narrator at every turn to refusing to even leave the office, to standing in a broom closet until you are declared dead. It's a game worth exploring to every end.
1: Bioshock.
Bioshock was probably the greatest surprise of all. I deliberately ignored it for a long time, deciding I knew all I needed to know from the fact that it was a FPS that took place in a town called "Rapture." I was so incredibly wrong. Bioshock, like Arkham Asylum, aspires to be greater than just a video game. While Asylum delves deep into Batman, Bioshock (and by extension, the series) has been delving into classical apocalyptic literature.
Bioshock muses on Ayn Rand and free will, all while being genuinely creepy (I frequently spent times watching the game going 0_0, which is rare for me) touching (I cried twice) and interesting. I haven't a single problem with Bioshock 1, making it my best game of all time.