Opinion concerning "anymore" vs "any more" divides roughly into three camps:
There is no such word as "anymore". It is simply a misspelling.
"Anymore" and "any more" are two ways of spelling the same thing, and the two have the same meaning.
There is a useful difference in meaning between the two.
About the first two camps, little more needs to be said. Either statement stands on its own and needs no elaboration.
The difference in meaning considered useful by the third camp is that "anymore" is an adverb meaning "nowadays" or "any longer", while "any more" can be either adverb plus adjective, as in "I don't want any more pie", or adjective plus noun, as in "I don't want any more."
The difference between the two meanings is illustrated in the sentence: "I don't buy books anymore because I don't need any more books."
The distinction of "any more" and "anymore" seems to be recognized by many, but not all, US users and by dictionaries published in the US. At least one British dictionary (NSOED/93) and some British users recognize "anymore" as an alternative spelling of "any more", but do not recognize a difference in meaning.
The adverb "anymore" is standard American English when it is used in a negative sense, as in "I don't do that anymore." It is a regional or dialectal usage, mostly restricted to spoken English, when it is used in a positive sense, meaning "nowadays", as in "Anymore I do that" or "I do that anymore."