Ice

"Its ancestral sword, Ice, was forged in ancient Valyria and has been passed down through the generations."

- Bran Stark

Ice was a Valyrian steel greatsword and an heirloom of House Stark. It was used both in war and on ceremonial occasions by the Lord of Winterfell.

Season 1
Eddard Stark uses Ice to behead Will, a deserter from the Night's Watch. Theon Greyjoy holds the scabbard, as Eddard draws the blade. He holds the sword before him as he passes the sentence. Later, Eddard cleans the sword in the godswood at Winterfell.

Ser Ilyn Payne, the King's Justice, beheads Ned Stark with Ice, on the orders of King Joffrey. He keeps the greatsword afterward.

Season 4
Ice is melted down on Tywin Lannister's orders by a Volantene blacksmith brought to King's Landing to make Jaime Lannister a new sword. However, due to Ice's substantial size, there's enough Valyrian steel to make two longswords. When Jaime asks about the source of the Valyrian steel, Tywin simply replies that the previous owner no longer needed it. Tywin Lannister also callously burns Ice's wolf-pelt scabbard.

The second blade is given to King Joffrey Baratheon as a wedding gift on the breakfast before the wedding ceremony. Of all the names proposed by the attendants, Joffrey chooses "Widow's Wail".

Jaime later gives his blade to Brienne of Tarth to aid her in her task of rescuing Sansa Stark. He reasons that it is appropriate for Ned Stark's daughter to be protected with a sword forged from her father's own sword. Brienne chooses the name Oathkeeper to honor the oath she swore to Catelyn Stark.

Season 6
In a way, Ice returns to the service of the Starks, when Brienne of Tarth swears her service to Sansa Stark, laying Oathkeeper at her feet.

In the books
In the A Song of Ice and Fire novels, Ice is a huge and impressive weapon forged out of Valyrian steel and has been in the family's possession for over four centuries. As a Valyrian-forged weapon, it never needs sharpening. Its blade has a dark and smokey appearance (instead of the appearance of common steel in the TV series). Ned uses Ice to execute the Night's Watch deserter Gared and also to sacrifice Lady. After his father's execution, among the demands made by Robb Stark in exchange for peace was that the sword be returned to House Stark.

In the books, it is actually the Qohorik blacksmith Tobho Mott who reforges Ice into two smaller swords at Tywin's order. The Free City of Qohor is famous for its blacksmiths, who still know how to reforge Valyrian steel (but not create new Valyrian steel outright). Thus while the knowledge of reforging it is rare, it isn't limited to only three living smiths, as Tywin says in the TV series.

For unknown reasons, Mott was unable to forge the two new swords in crimson as Tywin ordered, no matter how much he tried, but in mixed colors of red and the original grey.

When Joffrey is presented with a new Valyrian steel sword by Tywin at his wedding feast (which he names "Widow's Wail"), Tyrion realizes that Tywin has had Ice melted down and re-forged. He regrets not returning the sword to the Starks when it was requested.