There used to be a couple giant spiderwebs and big rubber spiders, but there was never a screaming man in either of the webs. The spider web scene was removed several years ago and was replaced with a scene that depicts a never-ending staircase (complete with ghost footprints that appear and disappear).
I could have sworn I've seen a photo somewhere in my Internet travels, but here is what Doombuggies.com has to say:
Originally Posted by doombuggies
The screaming man in the spider's web: Did he ever exist?
Early in the days of the Haunted Mansion, rumor has it that there was a scene somewhere near the loading area at Walt Disney World's Haunted Mansion that showed a man trapped in a giant spider's web. While DoomBuggies.com has not yet discovered tangible proof of this claim, there are witnesses to the spectacle. Magic Kingdom Haunted Mansi0n Cast Member Shawn Potts delivers this account: "Long ago when the Magic Kindgom first opened, there was a man trapped in the spider web to the right of the Doom Buggy path, near the Grand Staircase. However, it was felt that this effect was too scary, which was probably due mostly to the fact that there was a hideous screaming sound that accompanied the effect. The man's figure was stashed under an Omnimover motor in the graveyard, and was often used to scare maintenance men. By the way... scaring each other was a very common pasttime for Cast Members at the Haunted Mansion..."
However, another second-hand account of the man in the web offers slightly different details. According to DoomBuggies forum member "RobotWolf," the man in the web "did indeed make it to the grounds at WDW, but according to my trainer he was never installed. He was still there when I worked there - circa '86, stashed in one of the concrete pits beneath an Omnimover motor. A neat bit of trivia to be sure. But I, personally, am glad that he was never used... wrong type of gag for a Disney attraction."
It should be noted that official records which document each sound effect utilized in the Mansion do not mention the scream of the man in the web, although there is some evidence on certain schematics that such a prop did exist.