man then are shocked to have him defined as being older.

I would count myself amongst the crowd who thinks Hamlet is older. I base my belief on the following conversation that takes place between Hamlet and the 1st Clown, who is the church sexton, a grave-digger, the church cleaner and bell-ringer.

Ham. How long hast thou been
a grave-maker?
1 Clown. Of all the days i' the year, I came to't that day that our last King Hamlet overcame Fortinbras.

Ham. How long is that since?
1 Clown. Cannot you tell that? every fool can tell that: it was the very day that young Hamlet was born,--he that is mad, and sent into England.
Ham. Ay, marry, why was be sent into England?
1 Clown. Why, because he was mad: he shall recover his wits there; or, if he do not, it's no great matter there.
Ham. Why?
1 Clown. 'Twill not he seen in him there; there the men are as mad as he.
Ham. How came he mad?

1 Clown. Very strangely, they say.
Ham. How strangely?
1 Clown. Faith, e'en with losing his wits.
Ham. Upon what ground?
1 Clown. Why, here in Denmark: I have been sexton here, man and boy, thirty years.

According to the preceding Act V.i conversation, the grave-digger has been in his occupation since the day Hamlet was born, which he eventually gets around to saying has been thirty years.

Some may argue that Hamlet must be younger since he is in college and he behaves so immaturely, but Gertude and Claudius don't behave much more maturly. Moreover, many people are still pursuing university degrees well into their thirties.

The above answer by rienzi is impressive, but it does not explain how Hamlet could have accumulated so much learning by the age of only sixteen or eighteen. Take languages. Hamlet knows Danish, of course, and probably has a speaking knowledge of Norwegian and Swedish. He must know English very well if he is being sent to England as an ambassador. Furthermore, he is speaking pretty good English in the play (although we are supposed to assume everybody is speaking Danish). In order to go to Wittenberg he would have to know German because it is a German university. To get into any good university he would be expected to know the Latin language and its extensive literature thoroughly, and he might even be expected to know ancient Greek. He would know French, of course, because that was the language of culture. And Shakespeare takes pains to show that the scholarly Prince has a thorough knowledge of Italian when Hamlet explains, evidently to Ophelia in Act 3, Scene 2, "The story is extant, and written in very choice Italian," demonstrating that he is not merely acquainted with the language but is a connoisseur of the language and the literature. Then, of course, Hamlet would have had to learn, not just the languages, but what the important books in all these languages contained

Shakespeare probably had a good reason for establishing Hamlet's age as thirty in Act 5, Scene 1. The Clown says he has been sexton here for thirty years and he came to it the very day that Hamlet was born. Richard Burbage probably starred as Hamlet when it was first produced, and Burbage would have been several years past thirty at the time. It is true that the part in the play seems to call for a young man, but there was no way Burbage could have passed for a youth. The article on Burbage in Wikipedia includes a portrait of the actor apparently painted around the same time he played Hamlet. Burbage looks well weathered--and life expectancies were, of course, much shorter in those days. Burbage was born in 1567 and would have been around thirty-five years old when Shakespeare's Hamlet first appeared.

It would have been difficult for an actor of only eighteen or so to handle a complex role like that of Hamlet. An eighteen-year-old would have been more likely to play Ophelia.