Harry Osborne, Mary Jane Watson, The Green Goblin, Doctor Octupus, The Kingpin, and (I think) Aunt May.

I believe that Wolverine also knows because of his enhanced sense of smell (whether he's friend or foe is the mystery, though ;o)). In one of the newer Spider-man novels, Peter makes reference to how Wolverine's known since he met Peter and Spidey in the same day.

July 2006 UPDATE: In what is quite possibly the most shocking and historical event in the Marvel legacy, Spider-man revealed his secret identity to the world as part of the Civil War storyline, which has been rocking the Marvel universe to its core this summer. So now, there's barely anyone in the world who doesn't know Peter Parker's alter-ego. We can only assume it will be a dangerous and hard life ahead for the old web-head. original answer as follows: As far as I know, here is a list of Friends and Enemies who know Spider-man's secret identity: Friends: Mary Jane, Aunt May, Harry Osborn (deceased), Felicia Hardy/Black Cat, Ben Reilly/Scarlet Spider (deceased), Wolverine Enemies: Doctor Octopus, Kingpin, Green Goblin I(Norman Osborn), Green Goblin II(Harry Osborn, deceased), Eddie Brock/Venom, The Jackal (deceased), Gaunt (deceased), Gwen Stacy clone, Kaine (deceased/unknown), Judas Traveller, Chameleon, False Richard and Mary Parker (Deceased), Rhino (Briefly in Spider-man's Tangled Web...no longer knows it) The following is list of people I am not entirely sure about: Professor Charles Xavier Daredevil Nightwatch (Retired) Hobie Brown/Prowler I Robbie Robertson (possibly suspects Peter's dual identity) Captain America Updated as of 10/26/04: The Fantastic Four does not know Spider-man's secret identity, even though they've helped him many times in the past (the problems with the symbiote being most notable). Reed Richards, out of respect and protection of his secret identity, has never seen Spider-man's face...not even Spidey's buddy the Human Torch! Professor X of the X-men MIGHT know, only because of his telepathy. I'll update this list accordingly. Hope it helps!

In addition to the characters previously mentioned, Captain America, Iron Man, and Spider-Woman all know that Spider-Man is Peter Parker. Check out the first few issues, specifically issues three and four, of "New Avengers" for details.

Just to confirm it, Daredevil and Spider-Man know each other's secret identities. They swapped identities some time during the "Death of Jean DeWolff" saga (Spectacular Spider-Man #107-110). Daredevil was able to figure out that Peter Parker was Spider-Man by his heartbeat, which apparently is a kind of auditory signature of a person's identity.