Pandemic's Mercenaries series, I could use another updated one of those. Just super dumb fun.
Tecmo's Deception series, I don't know why these never really caught on. The idea of all-trap based combat always activated that Looney Tunes comedy sense and I found it really entertaining.
I'd like to bring a lot of Lucasarts games back. But rather than harp on XWing like I usually would, let's say Outlaws. Classic shooter, classic western story, frankly amazing western soundtrack.
Let's go really, really obscure... Quarantine. This was a DOS-era driving game, dystopia future, open world, driving combat... and you are just a cab driver trying to get passengers from a to b alive without being blown up because everyone has wheel spikes, guns, and cowcatchers on their cars. Kind of Rogue Tripish...
Oh... Rogue Trip, Twisted Metal with less stupid "MK Tournament, but with cars" story and more silliness because the whole concept is silly anyway.
And finally, Pigskin Footbrawl. It was a weird, weird mix of football, Arch Rivals, with a kind of partial endless runner control scheme, and a fantasy setting.