How many Spider-Men / Spider-Women (Spider-Persons?) do we know exist in the Marvel universe?
17 "Spider-" prefix heroes, +2 with variant prefixes, +7 with "Spider" in the name
By my count, there were 12 before the Spider-Verse storyline (where many alternate-universe equivalents to Spider-Man were met) and another 5 met during it. There were also 2 that had variant prefixes (e.g. alternate spellings) and 7 that had Spider in the name, but it was not a prefix. In many cases, multiple heroes have taken on a role.
- May "Mayday" Parker, daughter of Peter and MJ
- Pete Ross, amalgam of Spider-Man and DC's Superboy (DC vs. Marvel)
- Oliver Osnick, a child who tried to be like Spider-Man
- Adriana Soria, creator of the Spider-Island virus
- Steve Rogers (Transformed by Spider-Island virus)
- Spider Hero
- Eric Brooks (a.k.a. Blade), created as a disguise
- Ben Reilly (Web of Carnage)
- Shathra, a being from the Astral Plane
- A spider-monkey version of Spider-Man (Marvel Apes)
- Peter Porker, a pig version of Spider-Man
With names that previously existed:
- Aaron Aikman, Patton Parnell, Cosmic Spider-Man, Cyborg Spider-Man, Hostess Twinkies Cakes Advertisement Spider-Man
- Gwen Stacy
- Penelope Parker
* Although her comic series is called Spider-Gwen, the character herself goes by "Spider-Woman".
- Billy Braddock
- Spider Moon-Man
- Spider-Punk (a.k.a. The Anarchic Spider-Man)
- Aunt May
Others with variant prefixes
- Peter Urich (Armor Wars)
- A satiricial version of Peter Parker (Not Brand Echh)
Others having Spider in the name
- Scarlet Spider
- Ben Reilly (Clone Saga), Kaine (Scarlet Spider vol 2)
- Steel Spider
- The Spider (Ultimate Comics: Avengers)
- Devil-Spider (a.k.a. Hobgoblin)
- May Reilly (Spider-Verse)
- Peter Parker (Spider-Verse)
- Old Man Spider (Spider-Verse)
While not a character, there have been several pieces of technology with the "Spider-" prefix or a variation on the name.
Frankly? Too many to list here.
But from the Wikipedia page on Alterntaive Version of Spider-Man, notable Spider-Folk include;
- Peter Parker, the original Spider-Man.
- Ben Reilly, a clone of Peter Parker who acted as Spider-Man for a time.
- Miles Morales, who took over the Spider-Man name after Peter Parker's death in the Ultimate Universe.
- Mac Gargan, the Dark Avengers version of Spider-Man.
- Jessica Drew, the original Spider-Woman.
- Dr. Otto Octavius, who acted as Spider-Man after taking over Peter Parkers body.
- Peter Parquagh, who is Spider-Man in 1602.
- Miguel O'Hara, who is Spider-Man in 2099.
- Pete Ross, an amalgamation of Superboy and Spider-Man called Spider-Boy.
- Hostess Twinkies Cakes Advertisement Spider-Man, a commercial purpose only Spider-Man who always defeats his enemies with Hostess-brand Cakes.
- And of course, Peter Porker, the Spectacular Spider-Ham, who deserves a full paragraph of explanation;
Peter Porker was born a spider (simply named Peter). He resided in the basement lab of May Porker, a slightly goofy animal scientist who had created "the world's first atomic powered hairdryer", hoping that "the introduction of nuclear fusion into America's beauty salons" would "revolutionize the hair care industry". After dousing her head with water and activating the dryer, May Porker accidentally irradiated herself, and in a fit of delusion, bit Peter, who then found himself transformed into an anthropomorphic swine much like May Porker herself. Running from the Porker homestead disoriented, Peter soon came to realize that he still retained a spider's abilities.
If you would have asked this question last year, it would have been easier to answer. Unfortunately, the Spider-Verse event created dozens of new spider heroes.
Peter Parker is your basic and Miles Morales came over from the Ultimate Universe. Right now, Jessica Jones (Spider Woman), Gwen Stacy (Spider Gwen) and Miguel O'Hara (Spider Man 2099) have their own comics. Cindy Moon (Silk) had a comic very recently, but I think it's cancelled now.
In recent memory, Doctor Octopus became Spider-Man in Superior Spider-Man. Ollie Osnick, who was a DocOck wannabe, became Spider-Kid and later Steel Spider. Scarlet Spider is a very messy one... I'll let you read up on it yourself.
Once Spider-Verse hit, there was a UK Spider-Man, Spider-Punk, Spider-Ben, etc. You can see a (not complete) list here: http://www.newsarama.com/20656-spider-verse-s-spider-men-we-try-to-name-them-all.html
However your question asks about the Marvel Universe, which just got destroyed, so most of those are technically not extant anymore. In the Marvel Universe there are only 4 (If you treat Secret Wars as having ended even though it's still going on but the sequels are already out). If you add the one who will be in the MCU, that makes 5.
Here is the wiki list: https://en.wikipedia.org/wiki/Alternative_versions_of_Spider-Man