The use of alright in place of all right has never been condoned by dictionaries or usage authorities, but this convention is not likely to last. Web searches already generate approximately one alright for every all right, and the brevity and versatility of alright is likely to overpower the clunkiness (in some uses) of all right.
Still, even though alright is closing ground on all right, the latter is never wrong and the former is still considered problematic by some. So if you came here looking for a simple answer, our recommendation is to play it safe and avoid alright. And if you must use alright, make sure it is an adverb (e.g., he dances alright), and use all right when the phrase functions adjectivally (e.g., everything is all right).
Or you can be bold and use the new word with no reservations, but don’t say we didn’t warn you.
Publications with high editorial standards have not abandoned all right—for example:
The Banks Are Not All Right [NY Times]
Shortstop Derek Jeter jokingly said he’d be all right, as if a 94-mph fastball to the side of a 38-year-old knee is nothing. [Wall Street Journal]
[I]t’s all right to be a bastard, as long as you have something original to say. [Financial Times]