In addition to its meaning of insanity or ludicrousness, crazy has taken on a slang usage in American English. In informal speech, the word has developed an adverbial meaning from its original usage as an adjective. Some examples:
Shit guys, it's crazy cold out there. We might wanna bring extra jackets.
That kid's folks're crazy rich. Absolutely loaded.
Careful, she's crazy pissed about that snark you made last night!
By an association of manic, raving behavior with insanity, crazy gained a general meaning of 'excessiveness' that eventually allowed it to function as a slang equivalent of 'really' or 'very.' In it's usage, it has a stronger undertone than its standard-language counterparts of something unreasonable, amazing, or over-the-top.
The development of an adjective into an adverb unmarked by the -ly ending is not unprecedented in the English language. Most people are familiar with the New England habit of using 'wicked' in this way. In fact, you could replace crazy with wicked in the first sentence above and retain the same meaning, though such a substitution may not be possible or common for the next two sentences.
While 'wicked' seems to be an independent development of the New England region, 'crazy' is probably a borrowing from African-American Vernacular English (sometimes referred to as Ebonics). AAVE frequently sheds the -ly ending of its adverbs due to a process of creolization that strips words of their morphological endings and alters word-order or sentence structure to recreate the same grammatical meanings, allowing adjectives to do double-duty without any modification. This does not constitute 'dumbing down' the language, just a development due to unique circumstances of contact and linguistic segregation of the African-American community. German, for example, also refrains from modifying its adjectives when they're used as adverbs (and no one accuses German of being a 'dumbed down' language, I can assure you).
A further extention of the AAVE conjecture demonstrates similarity and compatability between the slang usage of crazy and that of 'bigass.' Bigass has a similar intensifying effect, and has branched into further forms like 'hugeass' and 'dumbass.' In fact, crazy and ass can be joined in slang usage to yield a combined meaning of the two--intensifying and suggesting insanity:
I'm a crazyass mofo. Watch yerself!
To the best of my knowledge, the general intensifying usage of 'crazy' is confined to relatively urban environments, and may be limited to the Midwest of the United States. I was utterly incorrect on that count. 'Crazy' has hit both coasts and the suburbs. If any noders know more about the slang's regional spread, I'd appreciate hearing from them.
Ichiro2k3 makes the double-whammy observation that he's heard it in suburban New England.
Milk notes, "Staten Island New Yorkers, at least, are fond of 'mad'."
vebelfetzer notes, "We use it here in Seattle the same way, as well as 'insane'. Insane has not yet become an adverb, but it seems to be headed that way. Online, alternate spellings/pronounciations are gaining popularity, particularly "crazeh"."