The Face of Boe was a male Boekind whose outward appearance was little more than a gigantic, humanoid-like head. Although he could only grunt vocally, he was able to communicate telepathically. (DW: New Earth)
History
The Face of Boe had the distinction of being one of the oldest creatures in the known universe. This caused him to be dubbed on some worlds as "the creature that God forgot". He was well known by the 51st century, since Jack Harkness commented on the fact that he once saw someone dressed up as the Face of Boe. (NDA: The Stealers of Dreams) In 200,000, he was featured on BAD WOLFTV, at which point he was pregnant with six children (Boemina) who died forty years later. (DW: The Long Game) In 200,100, he was the focus of a question on The Weakest Link, where he was described as the oldest living creature in the Isop galaxy. (DW: Bad Wolf)
In the year 5.5/Apple/26, the Face of Boe was the sponsor of an event to safely witness the destruction of the Earth by the expansion of the Sun. The event was sabotaged by Lady Cassandra, but the Face was among the survivors. (DW: The End of the World) By 5,000,000,023, the Face was hospitalised in Ward 26 of the hospital run by the Sisters of Plenitude on New Earth. Apparently dying of old age, the Face summoned the Tenth Doctor to his ward. When a novice told the Doctor the legend of the Face's last words - a secret which the Face would impart only to one like himself - the Doctor realised that he fit the description of the "wandering traveller". (DW: New Earth)
The Face of Boe eventually recovered, saying that although he had grown tired of the universe, the Doctor had shown him a new way of looking at things. The Doctor asked about the message, but the Face told him that it could wait for their third and final meeting, and teleported away. (DW: New Earth)
The Doctor was ultimately reunited with the Face of Boe one last time during his travels with Martha Jones, in the year 5,000,000,053. Boe revealed his last secret with his dying breath after sacrificing himself to save the city of New New York: it was that the Doctor was not alone. The Doctor dismissed this, as he still firmly believed that the Time Lords were gone forever, and he was the last of them. (DW: Gridlock)
After the death of Mr. Saxon, Jack Harkness said he lived on the Boeshane peninsula, where he was a poster boy and nicknamed "The Face of Boe". This seems likely he becomes the Face of Boe, as since he can never die, he might just turn into a massive head (when the Doctor aged artificially, he was reduced to a small creature that resembled Gollum). (DW: Last of the Time Lords)