Map Games are a type of Shared Worlds game in which a map is posted, and then other people add to it, either showing the events of a year in a regular map game, or add countries. You can find the current overview of new map games in this thread.
The first thread to display the “map game” moniker was Crayhistory's ASB Colonisation Map Game, although it was preceded by the first three Map Continuations, which have only acquired the “map game” designation retroactively.
Some examples of popular map game types and series (and of the individual games within them) can be seen in the lists below :
ASB Colonisation Map Game by Crayhistory (finished)
End of Dystopia Map Game (finished)
End of Dystopia : 2154 Divergence (finished)
Principia Moderni (1900 Map Game) by coldblood11
Map Continuation I (finished)
Map Continuation II (finished)
Map Continuation III (finished)
Map Continuation IV (finished)
Map Continuation V (finished)
Map Continuation X (finished)
Map Continuation XI (finished)
Map Continuation XII (finished)
Map Continuation Z (XIII) (dead)
Countries of an Alternate World by theReturner (finished)
The New Countries of an Alternate World by Hominid (finished)
3rd Countries of an Alternate World by Zuvarq (finished)
4th Countries of an Alternate World by Monopolist (finished)
5th Countries of an Alternate World by Nusantara (finished)
Countries of an Alternate World - Triple Alliance Victory in WWI by theReturner (finished)
Countries of an Alternate World Zeta by Zuvarq (finished)
Countries of an Alternate World Zeta Two by Zuvarq (finished)
Countries of an Alternate World* by Muwatalli' (finished)
Countries of an Alternate World 2* by Muwatalli' (finished)
Countries of an Alternate World 3* by Muwatalli' (Dead)
Countries of an Alternate World 4* by emperorharry86 (Dead)
Countries of an Alternate World with a Cold War POD by Baconheimer (Dead)
Countries of an World with a Civil War POD by PiratePartyist (Dead)
The Countries of an Alternate World with a 1914 POD by PiratePartyist (finished)
Countries of an Alternate World : From the Beginning by le man (Dead)
Silent Map Game by Hominid et al (the original)
Dark Ages, created by CDA et al
Rise of Islam (632), created by PiratePartyist et al
Fall of Rome (476), created by Spitfiremk1 et al
Ancient World (1300 BC), created by Zuvarq et al
City Map Game, created by Baconheimer et al
Settlement & City-building Map Game, created by Zuvarq
We're an Unbuilding Team : City Construction Game, created by Mr. Magi et al.
The Long Build - English City Game, created by Orsino et al.
Navigare Occidentem : A Colonial City Game, created by tubendo et al.
Fictional ISOT series, created by scholar et al.
PISOT, created by pieman97405 et al.
AKISOT, created by AK47Productions et al.
Tossed Through Crosstime, created by Midnight-Blue766 et al.
LAISOT, created by lordapocalipsis et al.
Bouvet and Tenerife ISOT, created by Alternate History Geek et al.