The Cardinal-Protodeacon, Cardinal Medina, announcing the election of Benedict XVI in 2005.
...qui sibi nomen imposuit [nomen]!
In the last 700 years, a relatively short list of names have been chosen by those elected to be the Successor of St. Peter as Bishop of Rome. If the next Sovereign Pontiff takes one of these names he would be (in order of how recently the name was last used noting in brackets the last year a pope who was elected took that name):
Benedict XVII [Last Benedict elected in 2005]
John Paul III [Last elected 1978]
Paul VII 
John XXIV 
Pius XIII 
Leo XIV 
Clement XV 
Innocent XIV 
Alexander IX 
Urban IX 
Sixtus VI 
Marcellus III 
Julius IV 
Adrian VII 
Calixtus IV 
Nicholas VI 
Eugene V 
Martin VI 
Boniface X 
Celestine VI 
Presumably one of these particular names will be used once more.
The first Bishop of Rome to adopt a new name upon his taking the Chair of Peter was Pope John II (533-555), whose birth name was Mercury [cf., http://www.newadvent.org/cathen/08421b.htm]. The last pope to retain his baptismal name upon election of Pope Marcellus II (1555) for whom Palestrina's Missa Papae Marcelli is named [http://www.newadvent.org/cathen/09641a.htm].
Speaking of which, here is a recording of the Kyrie from that setting of the Mass:
If you are looking for more information on some of the recent pontiffs (after 1878) -- look no further than here: http://www.vatican.va/holy_father/index.htm
Meanwhile, this site gives a complete list with biographies of the popes through the ages:
This site gives a good list of the Bishops of Rome since the 13th century, with some susinct information on their background, titles, and dates: http://www.catholic-hierarchy.org/diocese/droma.html
So, who will the Conclave of 2013 add to the list?