Although there may have been many such, only three are named as "Half-elven":
E?endil would rather have chosen the kindred of Men, but he chose the Elves for his wife Elwing's sake, who chose the Elves. E?endil's fate was special however: he was not allowed to stay in Valinor, but had to sail the heavens in his ship Vingilot? the Silmaril of Beren and L?hien on the prow, as a sign of hope for Middle-earth. Elwing built a tower in the Shadowy Seas and often met him on his return.
The heirs of Elrond, including Arwen Und?iel, also had the free choice of kindred, therefore Arwen could choose to be counted amongst the Edain even though her father had chosen to be counted as Elven. The heirs of Elros were not given this choice, but their lifespan was enhanced many times that of normal Men. In later times the N?en?ean Kings, descendants of Elros, regretted their forefather's choice, and this helped lead to the Downfall of N?enor.
Dior was the son of Beren and L?hien, and he was therefore also counted as Half-elven, as were his children with the Elf Nimloth of Doriath, Elur?, Elur?, and Elwing. Elur? and Elur? were killed, but even though Elwing was given her choice of kindred she nor her brothers or father are called Half-elven by Tolkien.
Arwen, daughter of Elrond married Aragorn heir of Elros, and thus the two Half-elven lines were merged in the Fourth Age. Their son Eldarion and their daughters were not counted as Half-elven, but rather as D?edain restored.
It was a tradition in Dol Amroth that Imraz? the N?en?ean had married an Elf, and therefore the Princes of Dol Amroth were of Elven descent, but they were not counted as Half-elven.