What's the oldest building in the world that is still in use (i.e. used for something other than a tourist spot).
Pantheon in Rome (126 AD).
Most of the older buildings in the Wiki list ( http://en.wikipedia.org/wiki/List_of_the_oldest_buildings_in_the_world ) are either not in use, or used as tombs only, or were reconstructed significantly.
The Epidaurus Theatre (ca. 300-340 BC), the Delphi theatre (4th century BC) and the Odeon of Herodes Atticus (161 AD) in the Acropolis of Athens (known locally as the the Herodeon), still fulfil their original purpose, all three are constantly used as venues for various festivals. The ancient theatre in Dion is also used occasionally.
The Colosseum (completed in 80 AD) could also qualify, while not in constant use as with the Pantheon that DVK already mentioned, it is used by the catholic church for the Via Crucis ceremony on Good Friday. Furthermore in July 2000 the National Theatre of Greece performed Oedipus Rex in the Colosseum.
Lastly, the remains of the Temple of Hera (590 BC, destroyed by an earthquake in the 4th century BC) in Ancient Olympia is the location where the torch of the Olympic flame for the Modern Olympics is lit. A continuous flame was maintained at the sanctuary of the temple during the Ancient Olympics, and the temple was also the location where the olive wreaths for the victors were displayed during the games.
The upper story of the Theater of Marcellus (ca 13 BC) in Rome is a block of apartments.
While not exactly a building, the Western Wall in Jerusalem ( http://en.wikipedia.org/wiki/Western_Wall ) is a site in which daily praying takes place. It was constructed around around 19 BCE.
The Roman theatre in Caesarea.
The tomb(s) in the Valley of the Kings that we have not found yet.
Over the period from the 16th to 11th century BC high ranking Egyptians were buried in rock cut tombs in the Valley of the Kings in Egypt. The purpose was to hold the remains and grave goods of these individuals in perpetuity. These building continue to perform this purpose until they are looted.
While many tombs have been discovered and their contents removed, it is a statistical certainty that at least one remains undiscovered. Any that are still undiscovered will still be performing their original role.
Sumiyoshi-taisha in Osaka, Japan was built in 211 AD. It is a full building (rather than say, a bridge), it is not in ruins, it is not a tomb, and it is still functioning today in its original usage (as a Shinto shrine). Pretty sure only the Pantheon is an older building still in use. I've seen a much older thing, but it's a tree - Te Matua Ngahere in New Zealand
Adaptation of old buildings for new purposes does that count? The oldest building still in use for it's intended purpose... The church Santa Sabina in Rome, built in 422 AD, hasn't been changed since it was built, and is still in use by the Catholic Church.
Most of the thousand-year-old temples in Angkor, Cambodia, still serve religious function among the locals.
The Tower of Hercules is an ancient Roman lighthouse near A Coruña, Galicia, in north-western Spain. The structure is almost 1,900 years old and still in use today.