Excalibur
Excalibur (or can be also spelled as Escalibor or Excaliber) is a legendary sword in the King Arthur stories.
According to the plot of Tomb Raider Legend, Excalibur is the name that Lara and her comrades use for various swords that were instrumental in shaping the course of human destiny. Lara first sees a sword of this description when she and her mother are stranded in the Himalayan Mountains in Nepal. When, many years later, her friend Anaya Imanu passes on a rumour of an ornate stone dais in a Tiwanakan temple in Bolivia, Lara is compelled to visit and investigate the dais in order to discover the truth of her mother's disappearance. From then on Lara is dedicated to discovering the location of various pieces of the sword, and also discovering the truth behind the supposed death of her once friend, Amanda Evert...
The pieces of Excalibur
First piece: The tip
The tip of Excalibur was recovered from the body of the Yakuza Kumicho Shogo Takamoto, who had adapted it into a staff for ease of use. Takamoto had stolen it from Waseda University, a prestigious Japanese institution. From the little he knows about it, it was supposedly recovered from one of the various Crusades that Christendom waged in the Holy Land. When used by Takamoto it gave off waves of brilliant green energy.
Second piece: The blade
The blade of Excalibur was taken from James Rutland. He carried it everywhere, using it as something of a fashion accessory. However, he is deadly serious when using it in combat. He uses it to slash fiercely at Lara - it also seems to improve his speed and agility and can even allow him to levitate. Rutland is ignorant of the piece's history, and neglects to tell Lara where he acquired it.
Third piece: The crossguard
The crossguard was recovered from a secret Soviet laboratory in Kazakhstan. The crossguard and various other more modern artefacts were recovered, presumably from the Crusades, perhaps from the Caucasus region of the then USSR. However it was clear that the other items were too contemporary for serious study by the scientists assigned to Project 'Carbonek'. The crossguard piece was instrumental in experiments involving Tesla energy, resulting in the deaths of several scientists. The rest were either removed by the KGB, or shut up in the laboratory. When Lara visits Kazakhstan, she must beat Amanda to the artefact first - and when she does so, it results in a wholescale destruction of the laboratory.
Fourth piece: The hilt
The hilt of Excalibur is taken from the tomb of King Arthur, in Cornwall, England. In following an ancient map from a shield found in Kazakhstan, Lara happens upon the tomb and searches it for the mausoleum of the Knights of the Round Table. Lara manages to remove the hilt from the mausoleum, and return to where Alister and Zip are waiting.
Fifth piece: The Ghalali Key
The Ghalali Key isn't exactly part of the sword, but it essentially connects all the pieces together. It was supposed to be in a temple in Ghana, but as Rutland and Lara both discovered, it was nowhere to be found. Later, Lara links an indentation between the crossguard and the hilt, and recognises it to be the shape of the brooch that her mother was wearing when their plane crashed in Nepal. Lara travels there and recovers it from the wreckage of their plane, and then goes to the nearby Buddhist monastery where a dais is located. There, in the place where Amelia Croft disappeared, Excalibur is reforged.
History
Describing the sword that Lara recovers as 'Excalibur' is inaccurate. Throughout the game we are treated to seeing the link between the swords and the daises - literally, the 'swords in the stones'. According to Arthurian myth, and as Alister Fletcher points out, Excalibur and the 'Sword in the Stone' were two entirely different weapons.
The sword in Tomb Raider Underworld
In the ending sequence of Tomb Raider Underworld, Lara finds Excalibur, as well as two scraps from her childhood diary, lying beside the ruined dais in Nepal, where she and Amanda were teleported to via the dais in Helheim. If this is the same sword, a useless copy, or even a fully functioning copy, is never explained. It is unknown if this is a plot hole or not.