Not so much in SO2. Only with the character profile images on the menu screen. No cut movies in that game.
If you have a copy, I don't see why you won't give it a shot. I've played both SO2 and SO3. There are differences, but not to the point where you'd like one but hate the other. Although the graphics in SO3 are better, so you may find them having the 'anime look'. Another game that comes to mind, also made by Tri-Ace, is Radiata Stories. And also, if you happen to like Valkyrie Profile, there's a prequel out for PS2. I could see that. I personally like #3's story the best, but was saddened by their obvious lack of budget by then. To me, XS3 had the potential to be almost Xenogears in terms of grandeur, but it had to be cut down in size.
So...play Persona 3 and 4 and just ignore the anime cutscenes? Pretend it is like Star Ocean 2...well, the original, not the upgraded re-release with anime cutscenes. Not like they make up the majority of the game in Persona (not exactly cheap to make, and Atlus isn't huge). I think the PSP version of P3 might have even gotten rid of the anime cutscenes (or some of them), but I can't remember for sure. But that's PSP, not PS2. But if it bothers you that much, play Shin Megami Tensei:Nocturne and Digital Devil Saga 1+2 (must play both...playing 1 without 2 makes no sense...literally). No anime cutscenes in those games. A lot of the things that make Persona great are also found in those games. Although each one has its unique take on game design and story. I agree with most of the games listed so far. Lots of great suggestions. Probably missing some, but I can't think of many off the top of my head.
Metal Gear Solid games are presumably the best ever. But I really like Indigo Prophecy/Fahrenheit (american/european title). Too bad that the american version is censored.
What about Tony Hawk's Pro Skater 3? Received a score of 10 from Gamespot. Only a handful of games have scored 10s. EVER.
DMC 1 was a great game and must have I say and DMC 3 was in fact a b**** of a game in the beginning. But, once you get going, it becomes much easier...you just have to get out of the first few levels. Other games I would suggest are MGS 2/3, Dark Cloud 1/2, and Onimusha 1/3. Socom was pretty sick too.
I love my PS2. Here's my "must play" recommendations. Though some have been mentioned already I'll say them again for emphasis: -God of War I -God of War II -Killzone (I had to find a used copy) -Black (crank up the sound system) -GTA: Vice City -GTA: San Andreas -Metal Gear Solid 3: Snake Eater (2 was good as well, but 3 is way better) -Ico (I had to find a used copy) -Shadow of the Colossus (this is the greatest game I've ever played. I can't explain why. I can't categorize it. But somehow, it transcended games. It's the only game I've had an emotional reaction and attachment to.) Some Honorable Mentions: -Lord of the Rings: The Two Towers & The Return of the King Both of these were fun hack & slash adventure games with some RPG customization of additional characters and skills to unlock. I don't hear them get mentioned too often, but I enjoyed them with decent replay value, and they can probably be had for cheap. -Star Wars: Battlefront I & II Play as Jedi or Sith, Empire or Rebellion, and kill everything. Forgot to add this: I bought component cables for my PS2 and I couldn't believe the difference it made. It allows some games to run in progressive scan but in ALL of my games, colors were more distinct; graphics were sharper. If you have a component-capable TV, get component cables for your PS2.
SO3 may have the most convoluted M. Night style twist in an rpg story ever, but it's a good game outside of that. Play it understanding that you're doing so for the gameplay first. It builds, greatly I think, on both the item creation and the battle system of SO2. The characters are just as unique and enjoyable to play as, also. Other good or successful RPGs: Persona 3+4, FF10+12, Disgaea 1+2, Suikoden 3, Dragon Quest 8, Xenosaga (only if play all 3) And another +1 for Zone of the Enders 2. There's a good video summary of the prequel in it also so you don't have to play the first one.
I don't think I saw Sly Cooper mentioned at all in this thread. The whole trilogy is great, but Sly 2 is my second favorite game of the generation. I also didn't see Psychonauts, which was my favorite game. Tim Shafer at his best. It's a fun and unique experience, and hands down the funniest video game I've ever played. EDIT: GTA has rightfully been mentioned, but Bully was another Rockstar game that was a lot of fun.
This is a very hard to find game from 2001, but well worth it. This one is great as well and one of the later, well-polished PS2 games.
Only one I would like to offer you from my experience with the PS2, some games of which I still can play on my backwards-compatible PS3, mister fade. I peepee wholeheartedly and with utmost respect on your RACING genre, dear sir, with this here suggestion: Spoiler It's only the BEST Simulator... I still haven't finished it... mostly 'cuz I have to sleep, eat, and poop sometimes.
