Hey, this is a list of some games (or game series) that I think everyone should play at least once. They're not in any particular order, and the list may be biased towards certain types of games as it has a lot to do with what I think of them.
At it's current stage, the list is far from complete, and I will add a bit to all the entries, and add in more games, as time progresses.

Spacewar

Spacewar. You know what it is. If you don't, then I feel sorry for you. It was the first computer game, even before Pong. (there is some evidence for earlier games, but Spacewar is what is usually considered as being first)
In Spacewar two people each control a ship, dogfighting around a star. Players had to be careful because the star's gravity was always pulling you in.
There is more to say on Spacewar, so this entry may be updated.

Commander Keen series

Everyone who has played shareware DOS games has heard of Commander Keen. Billy Blaze, 8-year-old genius travels the universe in his Bean-with-Bacon Megarocket he made using his Mum's old vacuum cleaner (heavily modified) for propulsion.
Commander Keen is a series of platform games, with settings from Mars to the Vorticon Homeword and beyond, fighting Martians, crazy vegetables, the Shikadi, and his nemesis Mortimer McMire.

Deus Ex

Deus Ex is a first person shooter with role playing elements. I imagine most people would have heard of it, and it seems to be the only game of it's type since System Shock 2.
In Deus Ex, you play a character by the codename JC Denton who has been augmented to increase his abilities. Throughout the game you can find "biomods" which, when fitted by a medical robot, improve certain abilities or give new ones.
Deus Ex has a great storyline with so many variations that everyone could play it differently.

System Shock 2

If you haven't heard of this game, then I feel sorry for you. Without System Shock, games like BioShock and Deus Ex wouldn't exist.
The game puts you in a spaceship with nearly everyone else dead. Most of the crew have been turned into hideous mutents, and the AI has gone out of control and thus you have to worry about it's security system too. You can find new weapons, and upgrade them, use a few phsyic powers and upgrade your cybernetics to make your job a little easier.
Also, this game is scary. It makes it onto my "scariest games I have ever played" list. At the start, you see oethr people get killed near you, and also the 'ghosts' sometimes pop up at unexpected times.
But I think the worst is when you have set off the alarm, and you are trying to hide from all the monsters chasing you. But that's only because I haven't got far enough to see some of the weird stuff SHODAN throws at you...

Lemmings

Everyone knows what Lemmings is. And it occupied much of our primary school years.
In Lemmings you have to guide little green haired guys called Lemmings to the "home", a little house thingy. You use climbers, blockers, diggers, floaters, etc in order to guide as many Lemmings as possible to the home without them getting killed by the various dangers.

Cave Story

Cave Story, or Doukutsu Monogatari, is a Japanese platform game with a lot in it. The first time I played it I was expecting what I consider a 'normal' platformer, like BioMenence or Commander Keen. I was wrong. It has a really in-depth storyline (which can be changed a bit depending on your actions), there are a lot of secrets you can find, and it is, well, very good. You have to play it to understand.

Bubble Bobble

I remember playing Bubble Bobble back on my good old Commodore 64. It was a really fun game where two little dragons went through 100 levels destroying enemies by blowing bubbles at them then popping the bubble that they were caught in.
I never went very far, and my best memories of the game was in 2 player mode (each player controls one of the dragons)
I always loved getting the umbrella.

Riptide

This was my favourite game for around a year when I was a child, a record for me (the only other game to get close was Deus Ex)
In Riptide you controlled a small submarine, with a smaller remote controlled sub attached that could get to areas that were inaccessible to your main craft. However, it had a very limited power supply, and if it ran out it would explode (which was very annoying as it was hard to get it back again and you needed it often). Your main sub had a limited air supply, and since you were only near the surface on the first level you had to find other sources of air (think powerups).
The storyline is that the evil Dr Riptide has caused all the sea creatures near by to mutate into monsters, and you have to fight your way through them to Dr Riptide's secret underwater lab in order to stop his plot to take over the world. Ok, so the gameplay is better than the story, but that's true with most games.

Prince of Persia

I'm talking about the orginal DOS game published by Broderbund here, not any of the newer want-to-bes like Sands of Time.
Prince of Persia is a platform game that plays differently from any other I have seen. It is mainly running around the different screens that make up each level, avoiding traps by jumping over pits and grabbing on to ledges, and also sword fighting the various dungeon guards in order to escape and save the princess from the evil Jaffar. And, you only have an hour to do it.
Prince of Persia is an excellent game, that people who like DOS games (or even some of the newer 'sequels') should play and enjoy.

Skyroads

This is the only game like it I've played. It is essentially a pseudo 3D 'racing' game, but instead of other cars, your aim is to just get to the end of the track without being destroyed or running out of oxygen.
Overall, I think it's an excellent game that everyone should have played at least twice.

Clyde's Adventure

Clyde's Adventure was a favourite game of mine for a short while as a child, it is a great puzzle based platform game. There are no enemies, instead you have to be careful since you only have a certain amount of energy which is used whenever you walk, jump, or fall too far. Luckily there are little things you can get to restore some energy. The aim is to complete each castle by collecting all the gems and the treasure and then make it to the exit, with only your wits and your magic wand to help you.
Once enough gems have been collected, new castles become available to complete. It took me quite a while to finish this game, but then I was fairly young at the time. It is a good game.

Notrium

I first started playing Notrium quite a while ago, the first version that introduced more than 1 player race. Although the only race worth playing was the human. Now though it has advanced quite a lot, the other races are worth playing and each one has a slightly different story line.
Anyway, the premise of this game is that you are the lone survivor of a destroyed spaceship and have just crashed landed on an alien planet, called Notrium.
You have to make tools or otherwise advance yourself in order to survive, and eventually find away to escape Notrium.
I really iked this game because you could make your own tools and weapons out of parts that are lying around on the planet. In fact, you pretty much have to (unless you are playing as the alien or the psionic which can't use weapons)
Anyway, you have to play the game before you can get what it's about. It has advanced quite far since I first started playing, but sometimes I go back to an older version when the game was smaller and the story wasn't so obvious. Partly because it was slightly easier (in my opinion) and also because I felt it was more open. Although the newer versions have a lot more features and things that are possible (even building a hover-bike) and are probably just as open if not more-so (especially for Human characters)

Operation: Inner Space

This was an awesome Windows 3.1 game. Excellent graphics, sound and gameplay, many people that have played it say that it was the best game ever made for Windows 3.1, and it works on versions of Windows up to and including Windows XP, which is awesome. Unfortunately it doesn't really work on Vista or Windows 7 because it's a 16 bit application.
The basic premise of this game is that the Inner Demon (main bad guy/boss) and it's viruses have invaded your computer, and you have to help defeat it by going through each directory on your computer collecting icons, killing viruses, and generally having fun. You're not alone in this, there are other ships doing the same, and sometimes you have to fight them to collect the icons. There are teams of about 4 or so ships each, so some are your team mates and others may like nothing more than to destroy you. And, the othere ships change behaviour depending on how you have treated themn in the past, which is awesome. Also sometimes a folder is a race course, with the winner collecting the icons.
Well, there's lots more I should probably write about this game, I'll probably add more to this entry later.
But, one more thing, back when Windows 98 was the new Windows, I had been playing the shareware version, and ran out of time and so could no longer play. That computer had to be formatted for some reason, so when we reinstalled, I put back on Inner Space becasue it's an awesome game and I wanted to play it again. But, it told me that I'd already used up my trial period! I was all like "What? How?" And I still don't actually know how it did it. I suspect that it either wrote information to the CMOS or to the unpartitioned space at the end of all hard disks... (these days it's 8MB) Still, this was the only shareware game that I have ever uesd that still said the trial had expired after a complete reinstall. And that was damned annoying. So, my advice, get the full game. Make many backups.

Quenzar's Caverns

Another Windows 3.1 game. This was one of the first games to be made in Visual Basic, and in my opinion one of the best. (VB isn't that good at anything, after all.)
I'll add more to this entry in a little while.

Games that didn't quite make it

Some games didn't make it on to the list above, and some of these I'll give a brief mention here. They didn't make it for various reasons, either there were better games I started playing at the same time, like with Eternal Daughter being beaten by Cave Story, others I think there are better games of it's type, such as BioMenace and Cosmo's Cosmic Adventure, still others are just because they didn't stay in memory, games like Dangerous Dave, Xonix, or Math Rescue. Some I thought weren't quite worth a mention, games like Paganitzu, which probably should be in the list but isn't.

If you don't succeed the first time, change the rules.
- CrisisSDK