Here are all of the Valyrian steel weapons that are known to exist as of Season 7 Episode 5 (info from awoiaf):
Blackfyre, the ancestral sword of House Targaryen, once wielded by Aegon the Conqueror, lost during the Blackfyre Rebellion.
Dark Sister, a longsword of House Targaryen, held by Visenya Targaryen, lost during the Blackfyre Rebellion.
Ice, the ancestral greatsword of House Stark. Captured by House Lannister when Eddard Stark was taken prisoner, and used by Ilyn Payne to behead Lord Stark at Joffrey Baratheon's command. After the Red Wedding and defeat of House Stark, Tywin Lannister had it melted down into two smaller longswords, one gifted to his son, Jaime, the other to his grandson, Joffrey Baratheon.
Oathkeeper, the first longsword made from Ice. Given by Jaime Lannister to Brienne of Tarth.
Widow's Wail, the second longsword made from Ice. Given to Joffrey Baratheon as a wedding gift, passed on to Tommen Baratheon. Now carried by Jaime Lannister.
Longclaw, a bastard-sword of House Mormont, given by Jeor Mormont to Jon Snow.
Brightroar, the ancestral sword of House Lannister, lost by King Tommen II Lannister when on his expedition to Valyria.
Heartsbane, the ancestral sword of House Tarly. Stolen by Samwell Tarly from his father in Season 6.
Lady Forlorn, the ancestral sword of House Corbray.
The "Catspaw Dagger". Wielded by an assassin who attempts to kill Bran Stark in Season One. It previously belonged to Petyr Baelish, but he claims he lost it in a bet to Tyrion Lannister. However, the ownership of the dagger when it was used by the assassin is never firmly established in the TV series. Given by Petyr Baelish to Bran Stark who in turn gave it to Arya Stark in Season Seven.
Red Rain, the sword of House Drumm, which was stolen by them in a raid. Given the name and coloring, possibly the ancestral sword of House Reyne.
Lamentation, the ancestral sword of House Royce, lost in the Storming of the Dragonpit.
Orphan-Maker, the ancestral sword of House Roxton. Its last known owner was Ser Jon Roxton.
Truth, a Valyrian steel sword last carried by Moredo Rogare of Lys.
Vigilance, the ancestral sword of House Hightower. Its last known owner was Lord Ormund Hightower.
Valyrian steel arakh owned by Caggo.
Valyrian steel axe reputedly possessed by House Celtigar.
Do all the Great Houses own Valyrian steel weapons?
[GRRM] Oh, there are more Valyrian swords than we have seen so far. Not all of them belong to the Great Houses. Lesser nobility would oft purchase one as well, for the prestige, and sometimes knights or even lesser swords would acquire one on the battlefield, after the original owner fell. But there have been no more made since the Doom of Valyria.
But there might be as many as 227 in Westeros
The Valyrian steel blades that remain in the world might number in the thousands, but in the Seven Kingdoms there are only 227 such weapons according to Archmaester Thurgood's Inventories ... - The World of Ice and Fire
Ice - Belongs to House Stark at beginning of the series, but is later reforged into
Oath Keeper - Given to Brienne of Tarth by Jaime Lannister to aid her on her quest to find the Stark sisters. Still in her possession.
Widows Wail - Given to Joffrey Baratheon and then later to Jaime Lannister. Still in his possession.
Heartsbane - Belongs to House Tarly. Last seen with Sam when he arrives at the Citadel.
Lady Forlorn - Belongs to House Corbray. Never seen in show, but is mentioned in special features.
Blackfyre - Originally a Targaryen sword that was passed along to a bastard son who later would form House Blackfyre based on the name of the sword. Mentioned in special features only and current whereabouts unknown.
Dark Sister - Another Targaryen sword that is mentioned in special features only and current whereabouts unknown.
Brightroar - Belonged to House Lannister, but was lost is Valyria when an old King of the Rock disappeared.
Longclaw - Belongs to House Mormont at the begining of the series. Jeor Mormont passes it along to Jon Snow during their time at the Nights Watch. Jon is still in current possession.
Honorable Mention, Dawn - Belongs to House Dayne and is wielded by the Sword of the Morning. The blade is not Valryian Steel but "forged from the heart of a fallen star". The last known wielder was Arthur Dayne who was killed at the Tower of Joy. Ned Stark returned Dawn to Starfall, where it will remain until another Sword of the Morning arises.
In the show we are introduced to, and shown, five Valyrian steel weapons in Westeros. It's possible that there are more (as there are in the books, where it is claimed that there are 227 such weapons recorded), but these have not been mentioned or shown to us, yet, in the show.
Ice - An ancestral, Valyrian steel greatsword belonging to House Stark.
Introduced in "Winter is Coming" (S01E01), in the hands of Ned Stark, last seen in "Two Swords" (S04E01), when it was melted down on Tywin Lannister's orders
After the Red Wedding, Tywin Lannister had it melted down and forged into two smaller Valyrian steel swords:
Oathkeeper - the first longsword made from Ice, it was given to Jaime Lannister, who gave it to Brienne of Tarth.
Introduced in "Two Swords" (S04E01), when Tywin was overseeing the melting of Ice, last seen in "Death Is the Enemy" (S07E06), on the hilt of Brienne of Tarth
Widow's Wail - The second sword made from melting down Ice, given to Joffrey Baratheon, passed down ceremoniously to Tommen Baratheon (though it is never mentioned or seen after Joffrey's funeral), Jaime takes to wearing it in Season 07 after Tommen's death.
Introduced in "Two Swords" (S04E01), when Tywin oversees its forging,
then given to Joffrey as his wedding gift (S04E02), then last seen for a while at Joffrey's funeral (S04E03), at which point it's implicitly passed down to Tommen, after which it is finally seen again in Season 07, wielded by Jaime,
who took it on after Tommen's death, last seen in "The Spoils of War" (S07E04),
when Jaime is fighting the Dothraki with it
Longclaw - A Valyrian steel longsword belonging to House Mormont, it was given to Jon Snow by Jeor Mormont
Introduced in "Baelor" (So1E09), when Jeor Mormont gives the Valyrian Steel sword that belongs to House Mormont to Jon at Castle Black, last seen in the hands of Jon Snow in "Beyond the Wall" (S07E06)
Heartsbane - The Valyrian steel sword belonging to House Tarly, which Sam Tarly took from his father's possession at Horn Hill.
Introduced in "Blood of My Blood" (S06E06), in Horn Hill being displayed as the possession of Randyll Tarly, Sam steals the sword and it is last seen in his possession, and he leaves Oldtown in "Eastwatch" (S06E05), so though we don't see it, it is presumably in his possession
Valyrian steel dagger - A nameless dagger which belonged to Petyr Baelish and was used to attempt an assassination on Bran. Petyr gave it to Bran who gave it to Arya Stark.
Introduced in "The Kingsroad" (S01E02), in the hands of an assassin attempting to murder Bran Stark in Winterfell, it is seen in the hands of Catelyn Stark, then Petyr Baelish, who then gives it to Bran in Season 07, and Bran finally gives it to Arya, who then gives it to Sansa, last seen in "Death Is the Enemy" (S07E06), when Arya confronts Sansa and approaches her with dagger in hand, only to pass it to her (it is now in Sansa's possession)
Here is a list of the Valyrian steel swords from "A Song of Ice and Fire" that characters hold on the HBO series, "Game of Thrones:"
Longclaw - House Mormont's sword, now carried by Jon Snow. Given to him by the 997th Lord Commander Jeor Mormont, the "Old Bear," after Jon saved his life from a wight in the book "A Game of Thrones." In the HBO series, this happens in *S1 E8. In *S1 E9, Jon is actually given Longclaw by Lord Commander Mormont.
It was his son, Jorah Mormont's sword, who was disgraced and the sword given to his father to keep. Jeor Mormont didn't like to look at it, as it reminded him of his son's fall from grace. Since the bear's head on the sword, (House Mormont's sigil) was damaged by fire in the fight, Ser Jeor Mormont had it changed to a wolf's head, with garnet eyes; representing Jon Snow's heritage from his House Stark, whose sigil is the Direwolf.
Ice - Eddard (Ned) Stark's** sword and the ancestral sword of House Stark.
Ice was used by Ilyn Payne to behead Ned Stark in King's Landing, at the order of King Joffrey Baratheon.
It was then melded to make for two swords for Tywin Lannister's family members: his grandson King Joffrey Baratheon, and one of his sons, Jaime Lannister. Thus, excluding his other son, Tyrion Lannister.
Widow's Wail and Oathkeeper were made from Ice.
Widow's Wail was held by King Joffrey for a moment before his death by poisoning in what has now been named by fans, The Purple Wedding. This happens in the book, *"A Storm of Swords" and in S4 E2.
Widow's Wail is now in the possession of King Tommen Baratheon.
Oathkeeper is carried by Brienne of Tarth, after being given to her by Jaime Lannister. He gives it to her in the book, "A Storm of Swords," "to defend Ned Stark's daughter" (Sansa). In, S4 "Oathkeeper."
Arakh - carried by Carggo Corpsekiller, a Dothraki sellsword.
Heartsbane - Sword of House Tarly. Held by Samwell Tarly, after stealing it from the house of his father, Lord Randall Tarly. We may see this sword in future episodes, as House Tarly will fight in the Battle of the 5 Kings, which will be part of upcoming seasons.
Vigilance - Sword of House Hightower, this may appear too in later episodes. It has been reported that Game Of Thrones will tell the story of the Tower of Joy in S6. Ser Gerold Hightower is part of that story.
There are many other Valyrian swords, axes & daggers in "A Song of Ice and Fire." They have been scattered and lost, but there are supposedly around 100 that have survived that exist now.
Some say the *dagger Petyr Baelish, aka "Littlefinger" carries is made of Valyrian steel.
Orphan-Maker - House Roxton held this sword in the S5, *"Dance with Dragons."
Joffrey had a Valyrian steel sword before he died. Tywin Lannister had made 2 Valyrian steel swords out of Ned Stark's huge sword; one he gave to Jaime, who later gifted it to Brienne of Tarth, and the other one was given to Joffrey as his wedding gift. If you remember during the Purple Wedding when Tyrion gifts him a book he uses the Valyrian steel sword to shatter it into pieces, but I don't know what happened later to that Valyrian steel sword.
It is not known from teh show, as this number or info was nowhere mentioned in the show. Also, it is not known from the books either.
All known Valyrian steel swords are held by great houses, but far be it from that every great house has one. Lannisters didn't have one until they took Lord Starks sword and made two smaller ones from it.
Also note that there is sword Dawn, that you could see in Tower of Joy event when young Ned Stark fought Ser Arthur Dayne. And later when Ned took it, that is the sword he placed near the Lyanna's bed (with symbol of star on the hilt). It is not Valyrian steel but meteor, or as Westerosi would say "magic stone". It is bright unlike Valyrian steel but is similar in quality. Perhaps we will see more of Dawn in fight against the night.