You’ll often you’ll see dates with apostrophes.  “The 60’s were an interesting time.”  “Home computers really took off in the 1980’s.”

Simply put, that’s wrong.  An apostrophe indicates possession – the girl’s dog, the Smith’s yard – or that a letter has been omitted, as in contractions.  That’s not what’s going on it dates, so there should be no apostrophe.  The 60s, the 1980s.  

It may look a little funny without the apostrophe, but you’ll get used to it.