Top 10 attacking players.

Actual top 10 is 

1. Joseph Blackburne

2. Paul Morphy

3. Rashid Nezhemetdinov

4. Gioachino Greco

5. Adolf Anderssen

5. Mikhail Tal

6. David Bronstien

7. Rudolf Speilman

8. Max Lange

9. Alexander Alekhine

10. Mikhail Chigorin

Post my modest list too

1. Poul Morphy
2. Rashid Nezhmetdunov
3. Mikhai Tal
4. Prince Andrey Dadian 

Duda deserves a mention.

Janowski should be in there somewhere.

There are some strong players in this list, but Beliavsky and Fischer weren’t known for their massive all-or-nothing attacks the way Shirov, Tal and Nezh were.

Dariusz Swiercz

nobody mentioned spassky. astounding.

This is true. Nezhmedinov is the greatest attacker ever. His attacks were more impossible than Tal's, he has couple of beautiful wins against Tal. Search Rashid Nezhmedinov on Youtube and you will get some beautiful analysis. Was he the most accurate attacker? No. But his games were more beautiful and fun than anyone  I've ever seen.

Fischer, Tal, Morphy, Anderssen, Kasparov, Magnus, Hikaru, Anand, Mamedyarov, & Wesley

Actually, in his youth Spassky was far more likely to play a sacrificial attack than Fischer ever was.

Fischer was a founding member of Pawnsnatchers Anonymous. He would much rather grab a pawn and defend against an attack than sac material for an attack.

Pretty sure Spassky was considered more dangerous than tal at one point. who was it that said it... I think it was 1970. If someone has that statement, please post it 

Yep. Everyone who mentions Fischer as one of the greatest attackers doesn't know anything about Fischer.

     One man's opinion:

Tal-Yes, some of his games were later found to be unsound. Sometimes it          took years of worldwide analysis to come to that conclusion, and the           best  players in the world couldn't counter his attacks over the board.

Morphy-Created the science of using positional factors to create his               attacks.

Alekhine-Legendary attacking genius who made subtle changes in some        opening variations to bolster long-term attacking chances. Interestingly,      he knew he could never beat Capablanca that way so he changed his          style for that one natch, took Capa by surprise, and won the                        championship.

Nezhmetddinov-All-out attacks at all times, sometimes successful against     world-class players.

Spassky-willing to try anything against anybody. An elite all-around                player, had some legendary attacks against the world's best.

Kasparov-Another great player in all facets of the game, he liked to keep        the pressure on until his opponents cracked and were overwhelmed.

Fischer-his opening repetoire was selected to give him long-term attacking

   (or counter-attacking chances. His techinque was so good that often all       his attacking pressure netted him was a pawn, or a serious pawn                 weakness he could go on to exploit.

Petrosian-Nobody could play defense like he did if they didn't see all their      opponents' attacks coming. He'd wait for them to get their pieces                overextended or tangled up, then he would pounce like a tiger.               

There are so many other fine attackers in chess history that I can't choose      any two more as definitely better than the rest.

1. Garry Kasparov 

2. Mikhail tal

3. Rashid nezhmethinov

4. Vishwanathan Anand 

5. Anatoly Karpov 

6. Alexei Shirov

7. Judit Polgar 

8. Magnus Carlsen 

9. Hikaru Nakamura

10. Bobby Fisher

Fischer’s entire style was based on targeting the opposing king.