In no particular order...
1: Skyrim (PS3): This game needs no introduction!
2: Suikoden 2 (PS1): Beautiful JRPG with a vast range of characters, and a deep story exploring themes of love, trust and betrayal. It's an RPG that focuses on war and politics rather than dark magic taking over the world and stuff. I love all of the games in this series, but this one is extra special because a lot of the dialogue often changed, depending on which characters you took along on certain missions. This really adds to the game's replay value, it's a really engaging RPG that keeps you hooked from start to finish.
3: Age of Mythology (PC): The only PC game I've ever really got into. I just don't use my PC for gaming. It's also the only RTS game I've ever played, as I've been a lover of Mythology for years, and this game really brings the myths to life. Build towns and temples and fortresses. Raise an army of soldiers and mythical monsters and heroes to fight alongside them. Invoke god powers. Tend farmlands and set up markets to build an economy. Play the story mode or set up your own custom game. Loads of fun!
4: Adventures of Alundra (PS1): This was an adventure game that was intentionally a rip-off of Zelda to appeal to fans of Zelda 3 on the Super NES. And to be honest, it's better than any Zelda game I've ever played. It's got a similar premise - you're this elf hero who has to seek out the help of 7 guardians and find magical weapons and items to overcome a lot of the puzzles, but this game really put the focus on the villagers who you are helping. you really get to know each of the villagers personally - kind of like a soap opera! And you explore loads of challenging dungeons in the waking world and dream world. It's not a very happy story either - lots of your friends get killed off in horrible ways!
5: Resident Evil Outbreak (PS2): A RE game that shows us the Raccoon City incident from the perspective of the civilians. It starts off like a normal evening - a group of strangers are enjoying a beer after work, then suddenly the pub is attacked by zombies, and you're thrown straight into this nightmare where you have to use your character's skilled to survive. Fight your way through the streets of Raccoon City, Explore the underground facility, escape from the hospital and the burning hotel and finally try to find a cure for the T-Virus in the Raccoon University. Lots of different endings to discover depending on how you play, and beautiful cut scenes.
6: Resident Evil Outbreak File #2 (PS2): Outbreak's sister game which gives extra scenarios, including a zoo full of infected animals, a subway crawling with zombies and monsters, an abandoned creepy hospital in Raccoon forest, the RPD police station (which gives us a prequel to events in RE2!) and an alternative ending scenario where you help Umbrella's employees try to escape and hopefully cure the virus. Gaming mechanics have been beefed up, with the ability to move while aiming and shooting. Plus elimination sub-games!
7: Vandal Hearts (PS1): Turn based RPG with battles set up on maps like a board game. As your characters become stronger through combat, you can upgrade their skills and abilities by giving them a new class. The story is just as engaging as the gameplay - you're fighting to avert a catastrophy from taring the world apart, and along the way, new characters join you and you learn a bit more about their past and how they fit into the story. The battle maps are a lot of fun - with villages beseiged by monsters, haunted ruins, heavily guarded strongholds and even skirmishes in other worlds.
8: Breath of Fire III (PS1): another beautiful JRPG from the PS1 era, this one features a small cast of characters who come together and want to learn the truth about why the dragons were driven to extinction. We're not saving the world or trying to liberate the land from tyranny, we're really just going on a long voyage of self-discovery. Along the way, we get to discover lots of different spells and skills, and use the master/pupil system to shape each character's attributes in combat. Very cute anime graphics and an adventure that manages to grab you and pull you in.
9: Suikoden Tactics (PS2): A spin-off game from the Suikoden series, this one admittedly has a crap story, but it's just so much fun! Instead of random encounters, you have maps where you set up your characters and have to use tactics to overcome your enemies. Suikoden's rune magic system works very well for this game, as some spells and weapon techniques let you damage different line ups of enemies. the interaction is very cool, as characters can actually chat with each other during combat, and doing this enables them to work better alongside each other - they can use combination attacks or defend their buddies when they are in trouble.
10: Suikoden IV (PS2): Yet another game from the Suikoden series, this was actually the least popular in the series, and quite rightly so, because the story wasn't developed as richly as the other games. But it does have it's good points. This game takes place on the high seas, and we gather heroes from all around the islands to help drive back an enemy invasion. The main character is afflicted with a cursed rune that drains his life force a bit at a time, and as the story progresses, we learn more about the rune's tragic history and how it affects the islands. There are some nice mechanics, including customizable sets of armour and sub games to earn prizes and strengthen your characters. Cutscenes have great voice acting and the beautiful seafaring soundtrack really gets me in the mood for a pleasant and unique adventure!