A clan is a group of individuals with a common ancestry.
In the Gargoyles Universe, the word "clan" usually refers to a group of gargoyles which defends a territory, including a rookery if present, and usually forms a protectorate of some sort. However, Macbeth also referred to his people in ancient Scotland as "Clan Moray," since the term can also be used for extended human families related by blood.
Ancient and Extinct Clans
We know of several clans that once existed, but have gone extinct. Goliath once said that at one point (probably while humans were still in the Stone Age) there were gargoyle clans all over the world. Gargoyles were the dominant species at that time, though it is unlikely their numbers ever equaled the current human population. It seems most, if not all, gargoyle clans were destroyed by humans one way or another.  Following is a list of extinct clans. Note that as Goliath's comment indicates, this list is far from complete.
- The Olympian Clan - Olympus, Greece - Destroyed sometime before 1996, and probably centuries earlier. 
- The Irish Clan - Ireland - Destroyed sometime between 10 AD and 1996.
- The Wyvern Clan - Wyvern Hill, Scotland - Destroyed in 994.
- The Scone Clan - Scone, Scotland - Destroyed by 1057 at the latest, and probably decades earlier.
- The Wyvern Clan (split) - Scotland - A branch of the original Wyvern Clan. Destroyed between 988 and 997.
- Demona's Clan - Scotland - Clan divided into numerous cells. Last cells destroyed in 1057.
Note: Many other clans in Ireland, Scotland and Greece may have existed besides the ones listed.
Several other locales that were possibly once home to gargoyle clans are theorized, though these are far less well known and their existence is only hinted as a possibility by Greg Weisman or by other clues where noted. These locales include:
- Africa - At least one clan existed here including a possible clan in Egypt. 
- Atlantis - Atlantis may have had a clan. The word "gorlois" and the creation of the Praying Gargoyle support this possibility. 
- Camelot - King Arthur's familiarity with gargoyles may have been in part due to a clan at his ancient castle. 
- Italy - At least one clan existed here including possibly one in Rome. 
- Middle East - At least one clan existed in Mesopotamia, including, possibly, a clan in Babylon. 
- Norway - At least one clan existed here, which makes sense given Odin's comment about not seeing gargoyles in Norway in recent times. 
- Persia - At least one clan existed here. 
- Various Mediterranean Locations - Gargoyles from other clans in this region may have joined members of the Olympian Clan in forming a clan on New Olympus. 
- Western North America - Though Grandmother said that gargoyles had never lived on Queen Florence Island, she is familiar with the species which may mean at least one clan existed on North America's Western coast.
Greg Weisman has stated that Antarctica has never had a resident gargoyle clan in the past.  This is probably due to the extreme day/night cycle and climatic severity, but it has been suggested that a gargoyle could eventually adapt to such conditions. 
The Surviving Clans
In 1993, shortly before Goliath's Clan was awakened there were only eight clans alive in the world.  They are all quite old, and have managed to survive by hiding from humans, living in extremely remote locations, or forming solid bonds with human allies.
- The London Clan - London, England
- The Ishimura Clan - Ishimura, Japan
- The Mayan Clan - ChacIxChel, Guatemala
- The Pukhan Clan - Pukhan, Korea
- The Xanadu Clan - Xanadu, China
- The Loch Ness Clan - Loch Ness, Scotland
- The New Olympian Clan - Mount Thanatos, New Olympus
- The Avalon Clan - Oberon's Palace, Avalon
It is unclear which of these clans is the oldest, but the Avalon Clan is probably the youngest clan and the New Olympus Clan is likely the next youngest because it was founded from other clans that existed at the time. Greg Weisman usually lists the clans in this exact order, so it is possible that they are in order of how old they are (oldest to youngest), though that is merely speculation. 
The First New Clans
The Wyvern Clan will be very traditionalist and in contrast, the Camelot Clan will be very internationalist. 
As the years go by, one can assume that the gargoyle population will continue to climb and more clans will be formed, once again bringing about a time when gargoyle clans are found throughout the world.