From Merriam-Webster’s.com (get the subscription – it’s totally worth it!)
“Q. Please explain which is correct usage: online and on line.
A. Merriam-Webster’s Collegiate Dictionary, Eleventh Edition defines online as an adjective meaning “connected to, served by, or available through a system and especially a computer or telecommunications system (as the Internet); also: done while connected to such a system.” This meaning is used in phrases such as “an online database” and “online shopping.” Online is also used as an adverb in phrases such as “shopping online” or “researched online.”
On line is defined in Merriam-Webster’s Collegiate Dictionary, Eleventh Edition as “in or into operation.” It is used in phrases such as “the factory came on line last year” or “the new system will be on line soon.”
Our research shows that the closed form online and the open form on line are the most common stylings used in these contexts. You should be aware however, that there is variation in usage, and on line will sometimes appear with the meanings described for online above, and vice versa. Also, the form on-line is not uncommon, especially with the meanings given for online above.”