Why did Ophelia kill herself in Hamlet?

One of the great unanswered questions about Hamlet is whether Ophelia did commit suicide, or if she was too far gone at that point and no longer capable of saving herself when she fell into the water.

Different productions will play it different ways. Look at her final speech - is it just gibberish? Or is it some sort of verbal suicide note?

OPHELIA

Indeed, la, without an oath, I'll make an end on't:

Sings
By Gis and by Saint Charity,
Alack, and fie for shame!
Young men will do't, if they come to't;
By cock, they are to blame.
Quoth she, before you tumbled me,
You promised me to wed.
So would I ha' done, by yonder sun,
An thou hadst not come to my bed.

KING CLAUDIUS

How long hath she been thus?

OPHELIA

I hope all will be well. We must be patient: but I
cannot choose but weep, to think they should lay him
i' the cold ground. My brother shall know of it:
and so I thank you for your good counsel. Come, my
coach! Good night, ladies; good night, sweet ladies;
good night, good night.

Exit