Here are memorable games/franchises for me personally:
- 007 Golden Eye
I only got to play this at a friend's house in Florida when I was a kid but the local multiplayer on this game was the best of anything out at the time. I still remember those good 4 player split screen marathons and one level where you could shoot the television on the ceiling to turn gravity off on the map.
- Fighting Force 64 (Fighting Force on PS1)
Probably my first real local co-op campaign experience, and one of those games you just have a blast from beginning to end. The environments were really interactive and all the stage bosses were satisfyingly difficult to beat. I still remember punching soda machines and gulping back a few cans of coke for a bit of health. I still remember picking up enemies and throwing them, breaking their back, or ripping bars and other objects from the environment to use as weapons.
- Test Drive 6
That intro will forever be burnt into my brain. Also the expensive twin jet engine car (Always paint it black of course).
- Resident Evil PS1 games
One of the first games to truly scare the hell out of me as a kid.
- The Legend of Dragoon
Far better than what I consider extremely overhyped Final Fantasy 7. It took some practice and skill to land attacks/abilities rather than simply selecting them from a menu, which for me made the game much more engaging and fun. For me, the story, art and music was also impressive and I enjoyed this game from beginning to end.
- SoulBlade/Soul Calibur
SoulBlade will forever be one of the most entertaining sword/fight games when I was a kid. I still remember some of those difficult levels with insane handicaps imposed on me like poisons, ringouts and time limits and reduced starting health. It was also one of the most fun local multiplayer games at the time for me.
- Twisted Metal games on PS2
While I must admit I never got the chance to try Twisted Metal after PS2 days, those days provided excellent local multiplayer car battle experiences for countless hours and I'll never forget that demonic Clown with his firey hair.
- SOCOM (especially the first 2 releases)
I think for a lot of console gamers this was the first major dip into online multiplayer & voice chat, which helped create a first-time experience that you can never get again. Similar to how drug addicts can never get a high as good as that first time (I don't use drugs). I still remember one of my first matches on the Blizzard map on SOCOM 1, where both teams ran to the middle and sorta looked at each other not sure if they were suppose to shoot the other team or not.
I played the first Killzone on PS2, as well as Killzone 2 on PS3 and beat both 100%, which says a lot when I usually get bored 40% into a game. They also had solid online modes.
- Final Fantasy 10
This was the first and most memorable Final Fantasy game I played. Honestly I enjoyed that game more as a kid than I enjoyed playing FF13 on PS3.
- Heavy Rain (and most likely future Quantic Dream games like Beyond: Two Souls)
One of the few games where the majority of players who have played it actually complete the game. For a game of this genre I feel your choices have more of an impact than any other game. It is engaging enough not to feel like a movie and a story that will emotionally draw you in. I will play any game of this genre if they can live up to the story and decision affecting interactive that Heavy Rain excelled at providing.
- The Walking Dead by Telltale games
This is similar to Heavy Rain's gameplay, but the choices you make have smaller impacts on the overall outcome. In my opinion Heavy Rain is definitely a superior game to this one, but the Walking Dead universe is what makes this game special, popular and memorable. I will definitely be buying future expansions/seasons of this from Telltale games.
There are tons of other games I enjoyed playing growing up, including local multiplayer on those PS1 WWE wrestling games, God of War, Metal Gear etc but the ones listed above standout more and remind me of why I love gaming so much and forever trying to find the next game that can meet or exceed those past experiences (and believe me it's difficult to find that feeling again).