Just to chime in with a dissenting opinion, it's worth mentioning that some folks find ARKHAM HORROR to be very, very cumbersome. It falls into that category for me of "Games I really wanted to like but just couldn't." There are tons of decks of different cards, tons of rules, and tons of maintenance and upkeep throughout the game. It's an amazing game, don't get me wrong. But playing it is more like work than fun. I say this as a Cthulhu/Lovecraft fan, a board game fan, and a die-hard horror fan.
I can see how one could view the game as such if not taught by an experienced player. I do think you are laying it on a bit thick as it sounds like complex boardgames are simply not your thing, which is fine. With a game of this size and scope of course the first bunch of playthroughs are going to be choppy when walking through the rules. There will be a learning curve. But that shouldn't stop the fun from happening unless the players do that themselves. At its core, the game is actually pretty simple but due to some poor wording in the instructions and on some of the cards a few complexities are present. Luckily there are tons of resources (many already linked in this thread) that clear up these rules gaffs and even more fan-made documents to speed up play and answer FAQ-type disputes.
As for the upkeep and maintenance, it is a step below Magic: The Gathering and D&D 3e/4e. Those phases are present but usually you are just flipping over cards and keeping track of modifiers that are in one of two places (the environment cards and the Ancient One's card). So if those two games are not up your alley as far as complexity goes, Arkham Horror probably won't be either.
Oh, and BTW, for what it's worth, ARKHAM HORROR has little in common with Lovecraft's Cthulhu Mythos in terms of theme. Lovecraft's stories are about ordinary fools who go insane because of the evil they glimpse; ARKHAM HORROR is about a group of investigators who go out killing monsters and taking monster trophies.
One can look at it that way or they can view it like the Call of Cthulhu RPG where your investigator is there to prevent horrible things from happening but has an equal chance of being devoured or going insane or surviving to see another adventure. Whatever works for each group or individual is the way to go. One could play the game more an RPG with characters playing more to their own goals and motivations and the game (especially with the expansions) lets that happen with ease.
Oh, and all that is without expansions. Once you start adding expansions, ye gods, it's like playing GURPS with all the Advanced combat rules and detailed terrain miniatures to go with it.
This statement is blowing the additional (and purely optional) rules modifications and game element additions
way out of proportion. The expansions add more options typically in the form of cards, making decks bigger and adding to the pool of Ancient Ones/Investigators. They also offer more options in the ways of board spaces (new towns to explore based on the Mythos!) and upping the difficulty level for more experienced players. The core game is MORE than enough to keep players going for dozens of sessions. I probably played about 30+ games before even cracking open the expansion because we kept getting our butts kicked and didn't want to add more fuel to the fire.
So, er, yeah ... I wouldn't even glance at the expansions until one was very well acquainted with the regular game. It is also worth mentioning that many of the cards (and there are many of them) don't come into play every game session.
This may be helpful to anyone considering ARKHAM HORROR:
YouTube - Arkham Horror video review
Not a bad intro to the basics! What no video can capture is the feel of the game as you progress through it. The dread around every corner and the elation of making a critical skill check at just the right moment. Or the crushing feeling of failure as the Ancient One awakens and you haven't the right resources to drive it away...
To finish up my post I'll just say that Arkham Horror offers the most replayability of any game boardgame I've ever encountered and answers well the first poster's question about these kinds of games. It falls under fantasy, sub-genre: horror. And it can be played solo, which is also a huge bonus in my book as that is a great way to learn the rules.