PS2 was by far my favorite game system last gen. Even though I started out last gen as a hardcore Dreamcast fanboy, by 2001 the writing was on the wall, and then I got news that Star Ocean 3 was coming to PS2 (SO2 being my favorite PS1 game ever)... so for Christmas 2001 I received a PS2, along with MGS2, Devil May Cry, and FFX. The system is a bittersweet one for me, not only due to it causing SEGA to exit the hardware business, it was also the last home console where Japanese developers really dominated (I vastly prefer Japanese games to western, as well as console gaming to handheld gaming), and was where videogaming started to turn into a pop-culture, dudebro activity (GTA series, Tony Hawk, all those now-forgotten thug-wannabe sandbox titles).
Rez - Sure, it was also on the Dreamcast, and has now been superseded by Rez HD on XBLA, but this was the first domestic release of the game. Which happens to be one of my favorites of all time. It's really the perfect melding of Tron-esque visuals and electronic dance music.
Dragon Quest 8 - Ranks with Skies of Arcadia as one of the best RPGs from last gen. This game did everything right, the beautiful cel-shaded graphics, immersive world, great story, beautiful music, and a high-point in voice acting. After the disappointing DQ9, I'm really hoping DQ10 goes back in this direction.
Shadow Hearts: Covenant - One of the funniest games I've ever played, with a great and unique setting, clever sidequests, awesome design where there isn't any missables (something tons of games can learn from), and a great timing-based battle system in the "Judgment Ring". Definitely one of the best RPGs from last gen.
ESPGaluda - My favorite STG of all time. The risk/reward system in place here, with the "Kakusei" time-slowdown mode is genius. The music is catchy and controls are tight.
Gradius 5 - Gradius has been a longtime favorite series of mine, the NES version of its spinoff Life Force was the first STG I ever played. And I'm a huge fan of Treasure. The game drags on for a bit too long, but it's a fantastic ride, with some awesome setpieces, sleek and beautiful visuals, and a good but uncharacteristically subdued soundtrack from Hitoshi Sakimoto.
Breath of Fire: Dragon Quarter - Another game with a Sakimoto soundtrack, oh wow. I was a few years late to the party with this one, but positive impressions from NeoGAF tastemakers and seeing it at Circuit City for $6 meant I had to get it. The combat system, like an SRPG without the grid, where you can set up traps for enemies, was great... not to mention the whole SOL system (I like to think SOL stands for "Shit Outta Luck" though

), where you can replay the game and see new events, was a cool concept. A lack of save tokens and oppressive difficulty kept this from being one of my favorites though. Yes I was one of those people who played the game through without starting from scratch or using my D-powers (up until the end, where I spammed the shit out of the bosses with them). It's basically the Vagrant Story of the PS2 gen.