The history of the Spider-Woman of Marvel Comics is a long one, so let's just begin from the start, shall we?
The original Spider-Woman, Jessica Drew, first appeared in Marvel Spotlight #32 and in a move unheard of today, never met popular superhero Spider-Man till her own title had more than 20 issues. She began her career as a HYDRA assasin, but refused to kill its long-time nemesis Nicholas Fury. Later, she made appearances in Uncanny X-Men and Avengers, where she was offered membership but declined, before playing a major role in the relaunch of Wolverine's series. She then disappeared suddenly from the Marvel Universe (though it was revealed in 1996 that she was trapped in another dimension).
Jessica Drew's powers include the typical super-strength and ability to stick to walls, as well as "venom blasts" (similar to that of the Wasp) which she lost during an Avengers storyline, naturally.
Meanwhile, in 1984, a new Spider-Woman appears in the midst of the Secret Wars. Called Julia Carpenter, she's every bit the Spider-Woman, complete with a costume that would inadvertently become the basis for the very popular Spidey nemesis Venom. Unlike her predecessor, Julia Carpenter chose to join the Avengers West Coast, and the team that formed from it - Force Works.
Julia Carpenter's powers are similar to that of Spider-Man, though her "webbing" is a result of her minimal psychic ability.
Then, in a move to confuse all readers, Julia Carpenter rescued Jessica Drew in the 1996 annual of Spectacular Spider-Man, thus allowing two Spider-Women to roam the Marvel Universe. However, Jessica Drew never wore her costume again, choosing instead to work as a private investigator based in the fictional Madripoor, while Julia Carpenter returned to the Avengers, but not for long.
In mid-1999, John Byrne set in motion events that would lead to the debut of a third heroine named Spider-Woman. Named Martha "Mattie" Franklin, she was a teenager who idolised Spider-Man. However, due to a twist of fate called the Gathering of Five, she was given almost unlimited power, allowing her to play the role of Spider-Man for a while before debuting as the "Spider-Woman of the new millennium". Unfortunately, her popularity was jeopardised by the more-popular Spider-Girl - the daughter of Spider-Man in an alternate future, and her title was canned after two years.
Mattie Franklin's powers are apparently limited only by her own teenage creativity. So much for "absolute power corrupts absolutely", huh?
As of this writing, Spider-Woman (all three of them) have yet to make any new appearances.
NothingLasts4ever suggests that the title character of the Marvel MAX adult imprint Alias aka Jessica Jones could be former Spider-Woman Jessica Drew. However, several discrepancies and the fact that the MAX universe has been labeled as non-canon discount this possibility.
Thanks to caknuck of the Typo Death Squad for correction of my previous spelling errors.