WALS Chapter 27 describes a number of functions for reduplication. All examples below come from chapter 27 unless otherwise noted.
Pangasinan uses reduplication to mark plurals:
Ilocano uses reduplication on nouns to mark a distributive plural:
sabsábong "various flowers"
Ilocano also uses reduplication to turn nouns into reciprocal verbs:
balembales "to avenge each other"
Chukchi uses reduplication to mark the absolutive case:
jokwat "eider duck"
jokwajow "eider duck (ABS)"
Kayardild uses reduplication to turn nouns into adjectives:
Yawelmani uses reduplication to mark associatives:
k'ɔk'ɔhis "one with large buttocks"
Luiseño uses reduplication to mark the number of an inherent object:
lawi "to make a hole"
lawlawi "to make two holes"
lawaláwi "to make more than two holes"
Mountain Arapesh uses reduplication to mark carelessness on the part of the subject or agent:
su "to touch"
susu "to touch all over"
Luiseño also uses reduplication to turn a verb into an adjective:
lepi "to tan, soften"
Ancient Greek used reduplication to mark the perfect aspect (Ancient Greek Press Book Chapter 42):
γέγραφ "have written"
Tigak uses reduplication to turn a verb into a person who regularly performs that action:
Turkish uses reduplication to mark intensity:
bembeyaz "very white"
Additionally, automatic reduplication is possible, where an affix requires reduplication of the root with no additional meaning. Chapter 27 gives this example from Ilocano:
singpet "behave" + agin-
aginsisingpet "pretend to behave"