As per most of the stories I know, witches usually burn when they come into contact with water.
Why is this so and what is the origin of this myth? Also,why do witches burn? What about wizards?
TL;DR This belief doesn't come from a myth. It first appeared in The Wizard of Oz.
I think the first time this belief was stated was in The Wizard of Oz rather than in any myths. The belief probably comes from older myths/customs surrounding witches that were drawn upon to create this idea for the Wizard of Oz.
Water used to find witches. This took 2 forms. A suspected witch would be tossed into a pond with feet and hands bound and if she floated she was a witch. A more likely origin for the burning in water idea though is a second method to find witches. The suspected witch placed her arm in boiling water the wound was then bound with a bandage. After a week the bandage was removed and if the wound was healed they were innocent as God had healed them. If not they were guilty.
Holy water was used to keep away witches. People would put holy water on their door to keep out witches. This happened in Catalan traditions as, at the new year, according to Catalan folklore, witches are supposed to come and steal children away unless precautions were taken including sprinkling holy water on entrances and exits.
Witches in Catalan folklore were often scared of water as washing them would reveal the devils mark showing them to be a witch.
On the other hand I doubt Catalan folklore had witches die in contact with water since a ritual to become a witch involved bathing in saltwater which would not be a safe pastime if water killed them.
As a follow-up to my (almost) namesake @Thom .
And to @Spencer
It is not specifically stated that they burn in water they are only afeared to cross it.
Tim O 'Shanter's poem says
Ah, Tam! ah, Tam! thou'll get thy fairin! In hell they'll roast thee like a herrin! In vain thy Kate awaits thy comin! Kate soon will be a woefu' woman! Now, do thy speedy utmost, Meg, And win the key-stane of the brig: There at them thou thy tail may toss, A running stream they dare na cross. But ere the key-stane she could make, The fient a tail she had to shake! For Nannie far before the rest, Hard upon noble Maggie prest, And flew at Tam wi' furious ettle; But little wist she Maggie's mettle— Ae spring brought aff her master hale But left behind her ain grey tail: The carlin claught her by the rump, And left poor Maggie scarce a stump.