Why is Hamlet so upset at Ophelia's funeral?

Act 5, scene 1, of Shakespeare's Hamlet begins with the Gravediggers (also known as Clowns) standing at a gravesite in a churchyard, discussing a burial. Within a few lines, we know that they're talking about Ophelia:

FIRST CLOWN: Is she to be buried in Christian burial that wilfullyseeks her own salvation?
SECOND CLOWN: I tell thee she is; therefore make her gravestraight. The crowner hath sat on her, and finds it Christianburial.
FIRST CLOWN: How can that be, unless she drown'd herself inher own defence? (5.1.1–7)

In the previous scene we learned from Gertrude that Ophelia had drowned, and now there seems to be some question as to whether Ophelia committed suicide or if her drowning was an accident.
The Gravediggers conclude that, if it was a suicide, and if Ophelia weren't a gentlewoman, then she wouldn't have a Christian burial, and she wouldn't be buried in sacred church ground. In other words, rank has its privileges.

SECOND CLOWN:If this had not beena gentlewoman, she should have been buried out o' Christianburial. (5.1.22–24)

This offhand remark proves to be true. A Priest tells Laertes that Claudius had to intervene on Ophelia's behalf so she could be buried in the churchyard.

PRIEST: Her obsequies have been as far enlargedAs we have warranty. Her death was doubtful;And, but that great command o'ersways the order,She should in ground unsanctified have lodgedTill the last trumpet. (5.1.219–223)

One of the Gravediggers tells the other to fetch him "a stoup of liquor" and sets about digging in the grave.
Hamlet and Horatio enter the scene and banter with the Gravedigger, and Hamlet learns in passing, as we already know, that the grave is being dug for a woman.

HAMLET: Who is to be buried in't?
FIRST CLOWN: One that was a woman, sir; but, rest her soul,she's dead. (5.1.13–132)

The irony of the situation is that we know whose grave it is but Hamlet does not.
The discussion continues with Hamlet, Horatio, and the Gravedigger (which includes Hamlet's famous remarks about Yorick's skull), until the Gravedigger apparently leaves the scene or simply stands off to the side. A funeral procession arrives, to Hamlet's surprise, and several lines are spoken between Laertes and the Priest before Hamlet realizes that the burial is for Ophelia.
Thus, Hamlet's surprise and sock that characterize his reaction to Ophelia's funeral should include consideration of the fact that, until her funeral, Hamlet did not even know that Ophelia had died, and it certainly must have come as a tremendous shock to him.
Furthermore, his reaction can also be understood as a manifestation of his regret, remorse, and guilt. The last time Hamlet spoke to Ophelia, he rejected her, cursed her, degraded her, and demeaned her for being a woman; he told her to go away and leave the world behind forever:

HAMLET: If thou dost marry, I'll give thee this plague for thydowry: be thou as chaste as ice, as pure as snow, thou shaltnot escape calumny. Get thee to a nunnery. Go, farewell. Orif thou wilt needs marry, marry a fool; for wise men knowwell enough what monsters you make of them. To a nunnery,go; and quickly too. Farewell. (3.1.144–149)

Now Ophelia is dead, possibly by her own hand, and Hamlet has to be wondering if his recent words and the way he treated her had anything to do with her suicide.
Hamlet's intense grief can also be seen as an indication of the love that he felt for Ophelia. Laertes, himself grieving over his sister's death, and having only recently become aware of her decline into madness, leaps into her grave. Not to be outdone in either his grief or his love for Ophelia, Hamlet leaps into the grave after Laertes, and they fight:

HAMLET: What is he whose griefBears such an emphasis, whose phrase of sorrowConjures the wandering stars and makes them standLike wonder-wounded hearers? (5.1.252–255)

Hamlet answers his own question.

HAMLET: This is I,Hamlet the Dane. (5.1.255–256)

This declaration is not, as it's often interpreted, a chest-thumping challenge to Laertes, but an expression of Hamlet's grief. "It is I," Hamlet is saying, "whose grief bears such emphasis" and whose grief astounds the stars and makes them stand still in the sky:

HAMLET: I loved Ophelia. Forty thousand brothersCould not, with all their quantity of love,Make up my sum. (5.1.270–272)

Overcome with grief, Hamlet takes it out on Laertes, which is Hamlet's way of impotently railing at the universe for Ophelia's death. Hamlet exits the scene, still shouting at Laertes and threatening dire consequences for Ophelia's death against no one in particular.
Surprise, shock, regret, remorse, guilt, grief, and love are the reasons why Hamlet was so upset at Ophelia's funeral.