There are many swords made of Valyrian steel. Can anybody throw light on how many are there in total in the known world?
As far as I can tell, in the TV show, there are four Valyrian steel swords still known (to the viewer, as opposed to the characters in-universe) to exist:
Longclaw (Jon Snow)
Oathkeeper (Brienne of Tarth)
Widow's Wail (Cersei Lannister, previously Joffrey Baratheon)
Heartsbane (Samwell Tarly)
Oathkeeper and Widow's Wail were made from Ice, a Valyrian steel sword that previously belonged to House Stark. Ice was reforged into these two smaller swords, one given to Joffrey Baratheon (Widow's Wail) and the other given to Jaime Lannister who subsequently gave it to Brienne of Tarth.
There is also a dagger that was used to try and assassinate Bran Stark (S01E02).