I know of a few instances when at G8 or similar protests, policemen (a) started the beat-up, (b) went ahead to beat the non-violent majority of the protesters, too, without or improperly distinguishing them from the violent ones. (That said, my view of the 'Black Bloc' and their violence fetish, even if against just shop windows, is entirely negative.)

most G8 protesters want the G8 to get more done, not less

Well, in a way agreed, though to my knowledge most G8 protesters want things done in the framework of other institutions, not a club of the richest countries('s governments).

I think we have there a different culture.

There are differences in culture, but not in the scale of violent protests. Though, on the German right, this is constrained to xenophobic attacks of the far-right and mostly to East Germany (think Rostock-Lichtenhagen 1992), while on the German left, the far-left Autonome was more active (think Chaostage, May Day mayhems in Berlin Kreutzberg, and some earlier nuclear transports). Looking back a bit further, let's not forget some quite violent protests against nuclear plants, against the third runway of the Frankfurt airport, and riots involving squatters (Joschka Fischer beating up a policeman!).

_{*Lunatic*, n.
One whose delusions are out of fashion.}