Dictionary.com provides the following usage note:
Despite the appearance of the form alright in works of such well-known writers as Langston Hughes and James Joyce, the single word spelling has never been accepted as standard. This is peculiar, since similar fusions such as already and altogether have never raised any objections. The difference may lie in the fact that already and altogether became single words back in the Middle Ages, whereas alright has only been around for a little more than a century and was called out by language critics as a misspelling. Consequently, one who uses alright, especially in formal writing, runs the risk that readers may view it as an error or as the willful breaking of convention. [link]