Today, April 23rd, is probably Shakespeare's birthday. There's no direct record of his birth, but his baptism was recorded on the 26th and this usually occured three days after birth. This is also the traditional day upon which it's celebrated, and were his birthday to become a international holiday as it should be then I'm sure the 23rd would be chosen (which means we'd get St. George's Day off in England). Still, it just goes to show that there are many enduring mysteries in the chronology of Shakespeare.
A lot is made about Shakespeare's "lost years", the period between 1583 and 1589 where we have little or no record about what he did, but I think this mystery is oversold. We want to know what he was doing in those years mainly because we want to know the genesis of his talents, but to assume that there was some tremendous event that occured in those years which made him into the genius we all know is likely just wrong.
There's an anonymous pamphlet of 1605 that speaks of "some that have gone to London very meanly", the wider context of which, including a reference to Hamlet, shows that this pertains to Shakespeare. Whilst we shouldn't read into it too much, it's easy to derive from this swipe that Shakespeare merely came to London to seek his fortune—we know that he was a very astute and successful businessman—so for example the story that he had to flee because he stole deer from Sir Thomas Lucy is almost certainly out the window, and I think anything else that's of similar scandalousness is unlikely too.
That isn't to say that Shakespeare wasn't... somewhat of a goer, and the only decent contemporary anecdote we have of him was of him entertaining a lady in the city, but again he doesn't seem to have ever stayed away from Stratford entirely for any large period at all. He frequently made trips back to buy property and visit his family, so if he were forced out he would've stayed out. Sir William d'Avenant claimed that Shakespeare would often stay in his family's inn, the Crown Tavern, in Oxford on the journeys.
The Haughton theory, that Shakespeare was a schoolmaster in his very young years, strikes me as odd but plausible, and may well account for the genesis that people are looking for: but even then you can't take it as accounting for the period directly after his marriage and directly before coming to London. That Anne was pregnant as they were getting married, and again with twins a couple of years later, points to the fact that he may have been kept busy in those years by quite the most obvious cause.