Not being much more than an occasional visitor to the world of gaming, I need to call in outside assistance whenever I want to do a game post. Luckily I happen to be related to an obsessive gamer who takes offense if I recommend any unworthy games. I asked him if there were any games that would fit the monster theme I’m currently exploring, and what follows in italics is his response.
Betrayal at House on the Hill is the correct answer:

Betrayal at House on the Hill 2010 edition is available from Card Haus for $29.95
It’s been out of print for a while, but it’s getting a reprint (rumored to have removed the one genuinely creepy card) this year. I’m surprised you’ve never played it, I’ve had it for years.
[So you make me play that stupid train game, Ticket to Ride, but forget to show me a game featuring a haunted mansion. The new edition of Betrayal at House on the Hill is being released on October 5. Actually I don't see any monsters described in the press release of the game:
Betrayal at House on the Hill quickly builds suspense and excitement as players explore a haunted mansion of their own design, encountering spirits and frightening omens that foretell their fate. With an estimated one hour playing time, Betrayal at House on the Hill is ideal for parties, family gatherings or casual fun with friends.
Betrayal at House on the Hill is a tile game that allows players to build their own haunted house room by room, tile by tile, creating a new thrilling game board every time. The game is designed for three to six people, each of whom plays one of six possible characters.
Secretly, one of the characters betrays the rest of the party, and the innocent members of the party must defeat the traitor in their midst before it’s too late! Betrayal at House on the Hill will appeal to any game player who enjoys a fun, suspenseful, and strategic game.]
Other, less correct answers:
Arkham Horror

Arkham Horror is available from Dream Land Comics for $41.97
Very similar game built on the Lovecraft mythos filled with lovecraftian monsters. Personally I think the game itself sucks, here’s what I think happened:
1. Self-styled game designer who’s actually just a huge Lovecraft fan furiously masturbates onto the blank pages of “rulebook” with no thought for game mechanics or fun.
2. Nerds assume anything with Lovecraft’s name on it must be high quality because knowing about him puts you in some sort of counterculture, superbrain clique.
3. Game sells a million copies and 10 expansions come out.
[Okay, so we're not recommending Arkham Horror.]
Touch of Evil
I’ve never played this, but I think it’s exactly what you want. The setting is 19th century European hamlet and the players play scenarios that pit them against classic monster villains like Dracula, Frankenstein, werewolves, etc.
[This game sounds pretty cool to me. Although I might rather be a monster than a monster hunter. Here's the description: A Touch of Evil, The Supernatural Game is a fast-paced game of fiendish creatures, dashing Heroes, and high-adventure. Each player takes on the role of a unique monster-hunting Hero, racing against time to stop the forces of darkness from claiming another foothold in the world of man. Only by investigating the town and building your Hero’s strength can you hope to hunt down the Supernatural Villain to his Lair and defeat him in an epic Showdown. Players can race Competitively to be the first to defeat the Villain and save the town, or they can work together Cooperatively to defeat a much stronger Villain.]
Thank you Michael for your input. Has anybody played these games? Can you think of a monster game we might have missed?