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Glorfindel of Gondolin
A noble Elf of Gondolin, who fled the Fall of that city with Tuor and Idril and whose battle with a Balrog in the Encircling Mountains secured their escape with their son Eаrendil.
Glorfindel of Rivendell
A noble Elf of Rivendell, who fought at the Battle of Fornost and, a thousand years later, helped Frodo Baggins and his companions to reach the House of Elrond and evade the pursuit of the Black Riders.
The Problem of the Two Glorfindels
With the possible exception of Tom Bombadil's identity (and - of course - the wingedness or otherwise of Balrogs), there is no more hotly debated topic than the ultimate fate of Glorfindel. Were Glorfindel of Gondolin and Glorfindel of Rivendell the same person?
The only real resource we have to answer this question is in The Peoples of Middle-earth (The History of Middle-earth Vol. 12): XIII Last Writings, Glorfindel. Christopher Tolkien dates the notes he gives here at 1972, the year before his father's death.
These notes clear up one question immediately: at the time of the writing of The Lord of the Rings, Glorfindel of Rivendell was not conceived as the same character as Glorfindel of Gondolin. Tolkien says, 'Its use [i.e. the name 'Glorfindel'] in The Lord of the Rings is one of the cases of the somewhat random use of the names found in the older legends ... which escaped reconsideration in the final published form...'.
(C) The Encyclopedia of Arda