Alright is an alternate spelling of the phrase all right, an adjective meaning satisfactory but not especially good, acceptable (The play was alright, but I wasn't thrilled by it.); in a satisfactory mental or physical condition ("How are you?" "I'm alright."); permissible, allowable (It's alright if you turn your paper in late as long as you notify the professor.). It can also be used adverbially, especially in the first sense (I did alright at the donut-eating contest, but I didn't win.) In a third sense, it can be used as a particle expressing agreement or willingness, similar to okay. ("Let's go to the movies." "Alright.")
To purists, "alright" is unacceptable, but it is in fairly common usage. It is listed in The Merriam-Webster Dictionary, the Oxford American College Dictionary, and the Oxford English Dictionary, but all three sources note that it is a nonstandard spelling, so I wouldn't recommend using it if you're trying to impress someone. However, I have been informed that the Wall Street Journal uses this spelling, and so does James Joyce. So if you use it and get corrected, you can argue that you are at least in prestigious company.
The Oxford American College Dictionary states that the shortened form alright did not appear until sometime in the late 1800's, unlike its cousins altogether and already, which appeared much earlier. Why have these other words become accepted contractions while alright has not? It's probably because altogether and already differ semantically from all together and all ready, whereas alright and all right's meanings haven't diverged. Yet.
Sources: The Oxford American College Dictionary, copyright 2002 by Oxford University Press, Inc., from which I paraphrased the definitions.
www.m-w.com, the online Merriam-Webster Dictionary
www.oed.com, the online Oxford English Dictionary
Several noders, who have messaged me with suggestions and helped make this node a better place. Thanks, guys. (edited 3/27/05)