I played the hell out of Sonic Heroes. I might just be nostalgic, but I don't recall too much being bad.
There's a little game Rockstar made back in the early 2000's called State of Emergency. It can be not-totally-inaccurately described as "Anarchist Rioting: The Game." It's shallow, gameplay revolves around little more than wanton vandalism and murder for scorepoints, and it's great for a little blast of stress relief. Just turn on invincibility and infinite time codes, find a grenade launcher and chuck those puppies through windows!
I wouldn't say it's a classic, though. It's sort of the equivalent of a B-movie, dumb fun that you don't take too seriously. Hilariously, despite all the shit Rockstar was getting in the media at the time about Grand Theft Auto being the antichrist, I'd say State of Emergency was even more gratuitous with its violence. You get straight up rewarded for bashing windows in, setting off explosives in buildings, and you're only penalized for civilian casualties occasionally.