I should have read the OP more carefully; gonna expand my list now to include more titles including multiplatform ones.
Ps1: Tekken 3. One of the greatest games of all time, and definitely what cemented for me for a long until the Ps3 era, one of my favorite video game franchises.
Rugrats Search for Reptar & Studio tour. The former was one of my first video games I ever had, but the latter is one that I had a lot more fun playing because of its variety. I even got to play it on Ps3 thanks to backwards compatibility.
Spyro the dragon. The only one in the OG trilogy I got to play, and nothing in 30 years beats the charm and soundtrack of this game, not even the color saturated remake.
Crash Team Racing. Of all the kart racing games out there competing with Mario Kart, this is the only one that held up for me.
Ps2: Need for Speed Underground 2. I understand that this game was criticized for a lack of cops, but this was my first NFS game and I loved practically everything about it. Since it was my first entry, no game in the series was as enjoyable most likely because of the police aspect that they added back in.
Harry Potter Quidditch World Cup. The Quidditch aspect of the Harry Potter movies were always the most action packed to me, so having a video game dedicated to the magic sport appealed to me a lot. I know there's a sequel out there now but I haven't touched it, and probably never will.
Ps3: Uncharted 2. Man, does this game make me feel nostalgic. It is also one of the greatest games of all time and one of the most important ever in Sony's history. IGN wrote a couple of pieces on it which I highly recommend for anyone else who's a big fan of it.
Call of Duty Modern Warfare 2. This and Black Ops 1 are probably where CoD peaked for me on Ps3, and they're the two I enjoyed playing the most. The former is what catapulted CoD to my most played video game series for a long time because of the multiplayer, but I'm probably never playing it again.
Red Dead Redemption. Both GTA5 & even 4 are probably more popular Rockstar games from Ps3's era, but RDR was so fun and different from games I played in the past in the open world genre, which they were already masters of. I still have yet to play Redemption 2, and I hope one day Revolver gets revisited.
Mass Effect 2. My favorite video game of all time. Enough said.
Yakuza 3: my first entry in the Like a Dragon series. It's hard for me to tell how the general fan base perceives it, seems less favorable to the rest the more that I try to look into it, but I still really loved it. I replayed the remastered Ps4 version on Ps5 and I noticed that the subtitles were different. Kazuma Kiryu is now most favorite fictional character ever, and not just in video games.
Ps4: Rocket League! I actually did play the original, Supersonic Acrobatic Rocket Powered Battle Cars and it was quite fun and it's great to see Rocket League being as widespread as it is now. This was not only a timed console exclusive, but might go down as the best Psplus launch game of all time.
Yakuza 0, or Yakuza 6. It's hard for me to decide between the two despite 6 having such better graphics, but 0 might have had the best story, which is where the series excels in the first place.
Ps5: Modern Warfare 2 was the last CoD I played heavily until Micros
oft made the announcement of acquiring Activision.