Lets see.. Most of the legends surrounding him that I'm familiar with have more to do with his knights and attendants than Arthur himself, but I'll give you a quick rundown of the ones I know. My source is Tennyson's Idylls of the King, which is a really good read. The stories vary depending on the source. Besides Idylls, other famous works of Arthurian lore include Le Mort d'Arthur, Sir Gawain and the Green Knight, and The Once and Future King.
Merlin and Vivien
Then, in one moment, she put forth the charm
Of woven paces and of waving hands,
And in the hollow oak he lay as dead,
And lost to life and use and name and fame.
Merlin is a powerful wizard who was trained by another wizard named Bleys. Merlin makes sure Arthur is rightfully crowned king after King Uther dies since there was confusion about who was the rightful heir. Some time after Arthur becomes the king and does some lofty deeds, Merlin falls in love with an enchantress named Vivien. Merlin knows that she is evil and wants to seduce and kill him, but he can't resist her charms because he's so hopelessly besotted with her. She begs and pleads for him to teach her a spell that he knows she will use to destroy him. He refuses because he doesn't trust her but eventually gives in after a while. When he teaches her the spell, she immediately casts it and traps him inside of a tree forever.
Tristram and Isolt
He spoke, he turned, then, flinging round her neck,
Claspt it, and cried, 'Thine Order, O my Queen!'
But, while he bowed to kiss the jewelled throat,
Out of the dark, just as the lips had touched,
Behind him rose a shadow and a shriek—
'Mark's way,' said Mark, and clove him through the brain.
Tristram is a knight who's in love with Isolt of the White hands, but she's married to a tyrant named King Mark. Isolt loves Tristram and hates Mark, so they meet in secret every now and again at Mark's castle. A secret meeting of lovers is called a tryst. One night when Tristram and Isolt are having their tryst, Mark sneaks up behind Tristram and murders him by splitting his brain in two.
The Passing of Arthur
To whom replied King Arthur, much in wrath:
'Ah, miserable and unkind, untrue,
Unknightly, traitor-hearted! Woe is me!
Authority forgets a dying king,
Laid widowed of the power in his eye
That bowed the will. I see thee what thou art,
For thou, the latest-left of all my knights,
In whom should meet the offices of all,
Thou wouldst betray me for the precious hilt;
Either from lust of gold, or like a girl
Valuing the giddy pleasure of the eyes.
Yet, for a man may fail in duty twice,
And the third time may prosper, get thee hence:
But, if thou spare to fling Excalibur,
I will arise and slay thee with my hands.
Arthur is betrayed by his brother Modred and gets a near-fatal wound in battle against him. Before he dies, he has his knight Sir Bedivere dispose of Excalibur by throwing it into a lake. Bedivere is hesitant to destroy the sword because he wants something to preserve Arthur's legacy. Instead of destroying the sword as asked, he hides it. Arthur somehow knows that Bedivere hasn't fulfilled his request and commands him to do it two more times. Bedivere finally throws it into the lake the third time around, but before it even hits the water, a mysterious hand comes out of the lake, grabs it, and pulls it under. The deed is done, so Arthur floats away on a barge with some ladies who try to treat his wound. The barge is headed to an isle where Arthur either recovers or dies. You never really know if he dies, so maybe he will return one day. Who knows?