This is a list that I have compiled of games that I actually own, have played, and would recommend to other people. I know there are a few other possible must haves out there, but I havnt played them and therefore do not feel justified in recommending them to other people.
So here you go, in no particular order.........well, maybe alphabetically.
Armored Core 2
Sometimes you just need to blow stuff up after a long and frustrating day. And nothing helps amplify this experience than blowing stuff up while flying around in a giant robot that is armed to the teeth. There are tons of parts you can acquire which lets you customize your tool of destruction to your own personal liking. You can paint it too.
Guilty Gear X2
Quite possibly the best fighting game I have ever played. All the characters have a unique feel and playstyle that can be catered to your personal tastes. Its fast paced, aesthetically pleasing, relatively balanced, and nothing is more satisfying than pulling off Chipps overdrive attack and landing it while playing with Jordan.
God of War
Not to be played in the presence of wee ones! This one is rated M and it means it! Sure, its linear, but at the time God of War came out, its method of play was different and new. Unfortunately, since it was relatively successful, everyone and their brother in law has decided to make a game with quick time events rather than coming up with something original themselves.
Its different, its weird, its fun. What more can be said of a game that plays Japanese pop music in the background while you roll anything and everything up into a giant ball. And when I mean everything, I mean everything, ranging from someones pet cat, to houses and skyscrapers.
Legacy of Kain: Defiance
Im a huge fan of the LoK series. Such is that whenever I am reminded that EIDOS is currently not working on another installment, a part of me dies inside. Its a different take on the whole vampire thing with an interesting setting, terrific voice acting, cool story, and fun gameplay that is split up between two characters that play very different from the other.
Metal Gear Solid 3: Snake Eater
This is a sneaking mission. Even after trudging through MSG4 on my PS3, I would have to say that this is the best installment in the series in addition to being a must have for a PS2 owner. The sneaking gameplay is fun and challenging at times, it has a great story line with a cinematic feel (its a Hideo Kojima game after all) and there are some truly innovative boss fights that you get to take part in.
Courtesy of Tim Schafer and Double Fine Studios. Psychonauts is one of the few games out there that wanted to do something different and unique. How is it unique? Well, youre a psychically gifted individual who gets sent to psychic soldier camp and after everyone elses brain is stolen, its up to you to get them back. You explore the strange lanscapes influenced by certain characters minds and personalities and even have a run in with a telekinetic bear!
Resident Evil 4
The best Resident Evil to date in my honest opinion. Rather than run around in a ruined city infested by zombies, you are in an isolated Spanish village where something aint right with the people who live there. The weapons have a cool method for upgrading, the game is filled with genuinely scary moments, and the voice acting in this installment isnt horrible!
Shadow of the Colossus
Another game that gets praise for being different. Its just you, your horse, and 12 gigantic bosses that you have to defeat. Nothing else. No annoying little trash monsters that you have to grind through to get to your objective. Each Colossi has a unique way of being fought and the art direction in this game is absolutely spectacular.
Zone of the Enders: The 2nd Runner
Another title by Hideo Kojima, but gone is the sneaking gameplay. Instead, you pilot a giant robot and lay waste to everything you see. Its more than just mindless destruction though, there is an interesting and engaging story, cool music, and you learn new weapons and attacks as you progress through the game.
There you have it. I would strongly recommend checking out any of these titles. They are definitely worth it and have earned the Jay Duke Seal of Approval.