In the 6th book, Hermione and Ron take the Apparition test, but Harry is too young. Hermione passes, Ron "just fails". Harry says to Ron (paraphrasing) "You can take it with me". By the time Harry is old enough to take it, they are already in hiding.
So, is there any canon evidence that they actually took and passed the exam?
There seems to be no evidence that they did.
They failed/couldn't take it and then pretty soon after went undercover and on the run. Hermione does seem to do the majority of the Apparating, or seems to lead the way, though Harry definitely does do it fully himself at least once, taking Ron and Hermione with him on this occasion. (When escaping the Ministry - the film makes it appear that Hermione is in charge here too, but in the book Harry grabs them and goes, though Yaxley still grabs Hermione and is able to follow).
Harry and Ron were breaking the law in this case, but they were about as wanted as can be at the time, and being caught just was not an option. Too much was at stake to worry about not taking every step possible. Fortunately for them, once Harry became 17, the Trace could not be used against them.
I'm guessing that they passed the test after the events of the books, as it should surely by this time be quite quick and easy for them to do so - unless after the events of the books their missing education and requirements for licenses like this one were all permanently waived.
@ThruGog had some pretty nice evidence up there, but I can offer proof that at least Harry did not pass the test: Since you have to be 17 to pass the test, and the Harry turns 17 in book 7, the day before the wedding (i.e, the day before the ministry falls and he goes into hiding) we know that he, at least, did not pass the test before the end of book 7 (excluding, of course, the epilogue)
