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[Japo]

First for you I'd say Abuse. Fast 2D platform shooter where you aim anywhere with the mouse.
http://www.abandonia.com/en/games/97/Abuse.html
EDIT: I didn't realize it was already suggested. Nice video!

Not very platformer, but what about the Crusader games:
http://www.abandonia.com/en/games/19...o+Remorse.html

There's a game exactly like Wolf but about Lions, made by the same people. More of the same but if you like:
http://www.abandonia.com/en/games/1020/Lion.html

"Platform games" is a very broad description, from your examples I guess you don't mean Mario-like? I could say Flashback and the like but those have many puzzles and you seem to want pure action?

"Fighting games" is equally broad, we could say millions. Any special characteristic that you like?

And what are your other requirements besides "classic", and what do you mean by that (year range)? There are millions of games that could be suggested to fit your requirements only for PC, and are you interested in other platforms?