Super Smash Bros. some think Sony did but I found All Stars nothing like Smash. It didn't have many iconic characters (Crash, Spyro, Croft, Old Dante, FF characters, Big Boss MGS3 style, Wander, ICO, etc.) and yet they paid up for advertising characters like Big Daddy, New Dante, and Raiden. Then they didn't do the percentage or ring outs and replaced them with only supers kill. The only thing on par or close to it was the stages. The studio just didn't get it. They were going to be accused of copying anyway they may as well have completely ripped off Smash, saved it for PS4 launch, and paid up for 3rd party icons (or the 3rd parties could be less stingy since it doesn't hurt anything and is free advertising for whoever's in the game). Superbot effed it up and it was the easiest concept to nail. Take Brawl, switch the characters out, switch the stages out, switch the items out, change nothing about the gameplay or modes, make it pretty and more capable online, profit.

Destruction Derby
Trap games like the Deception series
Would love more games to rip off Trials. I know Sony or someone tried with Urban Trials and there are tons of shitty shitty flashed based similar games but a time trial friends based game of its kind with maybe more than motorcycles would be cool.

Age of Empires 2. Even Ensemble Studios couldn't rip themselves off properly for Age of Empires 3, the only game that came close to the style of Age of Empires 2 was Star Wars: Galactic Battlegrounds.

Have you tried the Serious Sam games? Sounds like they're exactly what you're after! There's also been a PC remake of Rise of the Triad which was released a few weeks back on steam :)

I think Saints Row has been a perfect example of how "cloning" a game can turn out to be something seriously special. I never really got on with GTA since it went 3D, and Saints Row 1 did nothing for me. But as soon as they  started taking the game far less seriously, Saints Row is now doing more for me than GTA ever did :D can't wait to try the 4th one.

I just love crazier games in general.

Try Sleeping Dogs: it's a mix between GTA and Saints Row. It has a serious story, but a wacky and crazy gameplay.

Red Faction. I'd love to see similar destruction used in other games. You could literally blow up and destroy most of the environments in there. I remember having so much fun creating tunnels with explosives in the multiplayer mode, and the singleplayer campaign because of this.

I've been meaning to try out Serious Sam. Maybe I'll get that bundle on Steam that comes with the two original games. Thanks for the recommendations :)

Serious Sam is awesome. It's just pure old-school glory. Oh, and it's hard. Very hard. But awesome at the same time. If you can, grab one and two, and then BFE, which is the third entry.

Muramasa / Kingdom Hearts

Kingdom Hearts proved JRPG players were ready for real action, if you keep an amazing storyline, and muramasa that 2D is still awesome.

And both proved ultra realism is not the only way to make a game look gorgeous (plus mirror's edge), and had great reception. Still, publishers don't seem to assimilate that info.

Suikoden,
IE the amount of having all those party members and the HQ.