Legend of Dragoon:
This is a severely unappreciated JRPG for the PS1. It had a brilliant battle system (with the number of hits determined by the number how good you were at timing your button presses), an encounter meter to increase the chance of an encounter as you continued to roam the area, a great plot, a stunning twist at the end of disc 1, and is 4 discs of a solid JRPG. Also, the Dragoon form makes the battles a whole lot more interesting and adds a new dynamic to the strategy.
Freelancer:
Freelancer is a Space Trading and Combat Simulation Game (Long Genre title) in which you are a merchant who travels across multiple systems dealing goods, fighting against enemy vessels, go through the twisty life of Edison Trent's life after his cargo ship gets destroyed on a space port that is attacked (with him barely escaping). There are some surprises along the way and although it has laughable voice acting, it has extremely solid gameplay and a strong modding community. It also had servers and LAN support, but there are only private servers since Microsoft shut down Digital Anvil.
Neverwinter Nights:
This game is a masterpiece that was fairly popular whenever it came out, but I feel was relatively forgotten whenever NWN2 was released. It was a game where you could make your own character and send him through the Forgotten Realms, searching for the cure to the Wailing Death. It had an extremely strong plot, wonderful characters, directly followed the D&D 3rd ruleset, and a great soundtrack. I remember the graphics being impressive for its time, but looking back, they look a bit primitive. Also, there is a vast class system that widely effects how you can/will play the game, ensuring that you will have a different experience every time you are willing to try something new. Also, it has LAN and had online servers, meaning that you could share this experience of a game with all of your friends.
I will have more games up later, but I need to get to bed.