Although sometimes considered improper English, it is a completely logical contraction. The words altogether and already are similar contractions that are widely accepted.
People that criticize the use of the word "alright" are probably guilty of scores of grammatical errors anyway, like everyone who speaks the English language.
It can also be used when questioning the wellbeing of another. However, this will almost always be preceeded by a word denoting that it is a question, e.g. "you".
N.B. If someone passes you and says "Alright", do not respond "Yes". There are a number of accepted responses, such as a simple "Alright", often followed by the person in question's name, the phrase normally spoken in a more assertive tone, as it is a response, not a question.
2. Alright Alex
4. You alright?
2. Akane: "Ranma, are you alright?"
Some people think that when someone says "Alright?" to them, they should respond with how they are. Do not do this. You will be exposed as an uneducated idiot,
Me: Um, I'm fine thanks.
Me: *dies in a hole all alone with no friends*