Well I'd say as Jimmijo pointed out that to me Jazz jackrabbit seemed more like Sonic.
The games Twist mentions were indeed good games too, but for me it's like there's still a lot of difference both graphics style and gameplay wise. In none of those games do you really shoot.
Actually if you take Trolls it was good graphics wrapped around a fairly uninspired platformer which (at least to me) made it fairly boring to play after a while. That isn't to say I stopped playing it though.