In The Fellowship of the Ring, Elrond tells us that he was present during the first War of the Ring, when Isildur cut off Sauron's ring finger and caused the Big Bad's first fall. Elrond is still alive to see the conclusion of the battle against Sauron. (Gee, must be nice, being an elf, what with the immortality and the beauty and the goodness and all.)
But Elrond does not directly witness the last battle at the Black Gate of Mordor. We've got a couple of theories for the reason behind Elrond's absence from the final battle of the War of the Rings. First, he probably has his hands full keeping Rivendell secret and safe. Second, he sends his sons Elladan and Elrohir to assist Aragorn in his struggles, so why go himself?
And third, the first War of the Ring was also the war of the Last Alliance, when men and elves came together to fight a common enemy. Now, the elves are fading and Middle-earth is growing more and more, well, manly. This time, Middle-earth's salvation has to come from the peoples who are going to take it over in the next Age: men (and hobbits, we guess). So Elrond takes a back seat in this conflict because it's only fitting.
Elrond's major role in The Return of the King is actually as Aragorn's father-in-law. He arrives in Gondor in June, along with his daughter Arwen (the bride-to-be) and Arwen's grandmother Galadriel (mother of Celebrián, who was Arwen's mother). Elrond passes on the Scepter of Annúminas, another old heirloom of Elendil's house. But he's there mostly to witness the wedding between his daughter and Aragorn. Once they are settled as King and Queen of Gondor, Elrond must part from his daughter forever. She has chosen to stay in Middle-earth as a mortal, while he will sail into the West and leave Middle-earth for good.
One last note about Elrond: finally, in The Return of the King, we get confirmation that he carries one of the three Elvish Rings of Power. We see Galadriel's in The Fellowship of the Ring, but it is only in The Return of the King that we see Vilya, "a ring of gold with a great blue stone […] mightiest of the Three" (6.9.67). (Gandalf, of course, has the third one.)
So that explains both how Elrond has been able to keep Rivendell as a refuge from evil for all of these years, and also why Elrond has to leave Middle-earth and return to Elvenhome. Even though the Three Elvish Rings of Power were not made by Sauron, they are still somehow bound by the Ruling Ring. Now that the Ruling Ring has been destroyed, these Elvish Rings of Power can't just be left lying around.