Yakuza 3
Yakuza 4
Yakuza 5 (Digital Only for English)

Yakuza 0 and Yakuza Kiwami are both on the PS4. :)

Ishin is good apparently, PS3 is in japanese though.

Ni no Kuni and the Ratchet and Clank Future games (Tools of Destruction and A Crack in Time)

I'd also like to mention Tales of Graces f, which has one of the best battle systems in any J-RPG ever but the story is kind of a mess and sometimes really cheesy.

I don't know what do people see in Tales of Xillia, I found it pretty mediocre in every aspect, at least Graces has a great battle system.

Didn't watch the video so maybe I'm recommending you something that you already have.

Doom 3 BFG Edition
Ratchet & Clank Remastered
Jak & Daxter Remastered
Hitman Absolution
Tomb Raider (2013)
Shadow of the Damned
Alice Madness Returns
Darksiders 1, 2
F.E.A.R. 1, 2, 3,
Condemned 2: Bloodshot
Max Payne 3
Dishonored
Bioshock 1, 2, Infinite
Deus Ex Human Revolution
Just Cause 2
Aliens Vs. Predator
Kingdom of Amalur: The Reckoning

I've played almost all of the games there, and that's a nice collection you have there already. Brings some good memories back. :)

I would recommend actually trying to finish some of the games first before buying a lot more, otherwise you'll end up with a large collection of games you'll never play.

After you're done with inFamous 1 and 2, I'd suggest you play through the Uncharted series as they're pretty much the signature PlayStation franchise. Then after Uncharted get and play The Last of Us which is an absolute must have for every gamer and is considered by many to be one of the best games ever made.

If you enjoy GTA IV, I'd strongly suggest GTA Episodes from Liberty City as they add some nice features such as, better bike handling so you don't fall off as easily, nitros, parachutes, automatic shotguns, explosive round weapons, sticky granades, nightclubs, new vehicles, incluping helicopter with rockets, and a tank, among other things. Also just having a lot more focused story modes (that intertwine with Niko's story), that are shorter without filler missions, so it feels more varied and pure fun.

There are a few obvious ones that are sequels to the games you already have (if you end up enjoying them), so I won't mention those. I also think you should play the ones you have first, before you buy more games in the series.

But I'll list a few others that are pretty mainstream:

Red Dead Redemption - Similar to GTA, made by Rockstar, but set in the wild west. Could be described as "Grand Theft Horse" and some people prefer it over GTA games. Consider getting the game of the year edition, as you will also get the Undead Nightmare, which is a standalone expansion with zombies.

Assassins Creed 2 - A great entry point in the franchise and often considered the best one by many. 

Demon's Souls - This is a very difficult and punishing game, but if you really get into it and spend a lot time it will be rewarding, and you will understand the "Souls" games hype. Alternatively you could try Dark Souls, as either will give you a good idea of the "Souls" games.

God of War 3 - A Playstation classic franchise. An epic hack and slash game with some of the largest and most epic bosses you'll encounter in a video game.

Mass Effect Trilogy - If you haven't played it already.

Ico & Shadow of the Colossus Collection - If you haven't played it already. Ico has not aged that well in my opinion, however Shadow of the Colossus remains one of the best games ever made, and is still amazing and unique to this day. Still nothing else like it out there.

Ratchet & Clank Future: A Crack in Time - Another classic Playstation franchise. This is arguably the best R&C game on PS3. The game has great colorful visuals, varied gameplay, and is incredibly polished. The humor in the game is great and has jokes for adults too. I mean the game used to be called R&CF: Clock Blockers during development, but sadly they had to change it, but do expect this kind of humor in the game.

Journey Collector's Edition - Includes all 3 PS3 thatgamecompany games (Flow, Flower, and Journey), but Journey is the one must play game there. Unique, emotional, masterpiece, all words to describe it. Journey is one of the most beautiful games of it's time and simply has to be experieced. This is the poster child of video games as art. Its soundtrack got nominated for a Grammy award (first of any video game). Won plenty of GotY awards (including DICE awards) despite not being a big budget title. Alternatively you can just download Journey on PSN. But, the collection should be almost the same price, you get them on a disc, and Flower is a beautiful and relaxing game as well.

I'll also mention some other games without going into detail. Some of these are not for everyone, so you can look into these and perhaps you find something that interests you: Heavy Rain, Resistance 3, Killzone 3, Little Big Planet 2, Metal Gear Solid: The Legacy Collection, Ni No Kuni, Wipeout HD Fury, Yakuza 4, ModNation Racers, Okami HD, Beyond Two Souls, MotorStorm: Pacific Rift.

I would also ask what other systems you have, and should we be actually recommending multiplat games (as there are a lot to recommed), for example if you don't have a gaming PC and Xbox 360?

I recommend hidden PSN gem indie puzzle platformer Archibald's Adventures, I played it on PSP and PC.

Darkstalkers Resurrection too

Dead space 2

Thanks so much for the feedback, the systems I own are in my sig.

Never played dem but I heard it is japanese GTA lmao Ill have a feeling I will enjoy it I will check dem out.