I think Alexander Alekhine...or maybe Garry Kasparov or...
who is the best chess player with aggressive playing style?

obvious picks Tal, Kasparov, and Alekhine, my favorite being Alekhine. however, I've found that Yefim Geller, David Bronstein, and Boris Spassky are also great players to study if you're looking for an aggresive style.

The best ever were Tal, Petrosjan and Spiellman.
The most aggressive player now?
I think Kasparov or Polgar.
But now the aggressive style is not a winning style, the positional battle are most common than a real fight in the keys squares.

The aggressive style may not be the winning style, but it is the style that most of us chess players love
sir,i agree with what you just said.

Alexi Shirov, Tal, Larry Christansen, Judit Polgar, Tatiana Kosintseva she can fight and throw a punch this game really impressed me:
http://www.chessgames.com/perl/chessgame?gid=1600844
I felt for Ms.Kosteiunk's King after this game he had a few bruises on his chin and a black shiner after this one (I wondered if Alexandra applied ice on it?)
Rashid Nezhmetdinov, Bobby Fisher, Alexandra Kosteinuk, Simon Williams, Alexander Alekhine, John Nunn, Frank Marshall.

Don't forget the late great Leonid Stein. Was an absolute master of the intuitive sacrifice for an enduring initiative.

I like Morphy for old school attacking chess. He was able to really get his pieces out on the board while pushing towards his opponent. However, the Evan's Gambit (which he was well known for) started to fall out of favor because of Be7 (Black) rather than pushing the Black Bishop to an a file position.
I'm a big Spassky fan. He has a solid old school opening (no matter what got thrown at him by his opponents) and was able to create so great attacking formations. Fischer is high on my list as well. Petrosian was a great attacker but built up his positions slowly like a python strangling its prey.
Then there is Ozzie Cobblepot, chess.com's own attacking genius. His name strikes fear in the hearts of anyone sitting down to face him. OK, Cobblepot gets my vote!

GM Serper, Check out the wikipedia artical on him then watch his notable game, the one where he sacs everything

The best ever were Tal, Petrosjan and Spiellman.
The most aggressive player now?
I think Kasparov or Polgar.
But now the aggressive style is not a winning style, the positional battle are most common than a real fight in the keys squares.
-1 Petrossian? Are you out of your mind?

But now the aggressive style is not a winning style, the positional battle are most common than a real fight in the keys squares.
I'm assuming you don't follow top level chess today.
who is the best chess player with aggressive playing style? Anyone know?