I am still seeing uses of on-line, though I think it is incorrect. For example:
A web browser enables a user to go on-line/online.
Can you tell me which is the more appropriate to use, on-line or online?
According to this Google Ngram, online is used more often:
The use has shifted over time to omit the hyphen. For example in 1950, the OED writes:
This was still the case in the 1970s:
However, now the hyphen has dropped out, so the usage is as follows:
So, the current usage favors online instead of on-line.
Both are acceptable; usage depends upon the audience you're writing for, and then your personal writing style/personal taste, in that order.
There are many words in English which can be hyphenated according to personal preference, and often hyphenation provides greater clarity over non-hyphenation. Generally, in formal, professional writing, the decision to hyphenate or not will be made by the editorial staff for which one is writing. At the academic level, however, this decision will be made either by the professor, or -- if not -- devolve to the author him/herself.
However, as simchona's N-Gram indicates, "online" is currently gaining preference over "on-line". For my part, I tend to use one or the other, depending on context and rhetorical aim. For instance, I tend to hyphenate when the word is used as a predicate complement ("I am on-line", "I need to get on-line"), and use the non-hyphenated version when it's just a straight adjective ("It's an online game", "Online accounts are down, right now"). But these aren't hard and fast, even for me; if I'm writing for younger audiences, I will tend to just go with "online", because that seems to be how things are trending with their age group.