Vice versa, meaning (1) in reverse order from that stated, (2) or conversely, is two words, with no hyphen. The adverbial phrase was introduced to English from Latin roots in the late 16th century, and it has proved useful ever since. Like other established Latinisms, it does not need to be italicized in normal usage.
Vice versa indicates that a statement is equally true when its subject and object are switched—for example:
America is popular in Australia, and vice versa. [The Economist]
Scientists warned that further research would be required to find out if humans were spreading the bug to cows or vice versa. [Daily Mail]
It’s quick to fly from Italy to Greece (or vice versa), but much more romantic and cheaper to catch a ferry. [New Zealand Herald]
Vice versa is often misused to indicate a logical reversal rather than merely a subject-object reversal—for example:
… I should spend more on the clothes I wear the most and vice versa. [letter to Wall Street Journal]
Technically, this means I should spend more on the clothes I wear and the clothes I wear should spend more on me, which is obviously not what the writer intends to say.
Good ones can make us all feel better, and vice versa. [Guardian]
According to conventional definition of vice versa, this technically says that good ones can make us all feel better and we can all make good ones feel better, which is obviously not what the writer means.
Still, it’s usually safe to use vice versa wherever there can be no doubting what you mean. And while these last two examples are technically questionable, most readers would have no problem with them.