Here’s a wiki of online shops where to get postcards, organized by country where they are based. Feel free to edit it to add your favorite shops to it too — just click the 
button underneath this post!
Australia 
Australia Postcards
Fishpond
Utopia Homewares
Belarus 
Belgium 
Canada 
aweedmark
Canada Post Postcards
CaseyofAvalon
Chapters
Crave Paper
mixeddogart
Postal Happy!!
sillustrates by Stephanie Simpson
The Friends of Algonquin Park
Czech Republic 
Estonia 
Finland 
Harjun Paperi
Inge Löök
Katja Saario
Korttien Talo
Mantelina
Minna Lehväslaiho
Minorpostcards
Postcard garden
Raijami
France 
Arbre aux 100.000 rêves
Blue Art - Carte d’art
E-Mages
Lulu Shop
Paper and Postcrosser
Papiers & Compagnie
Planète Images
Woodhi
Germany 
Ampelmann.Shop, Berlin
Art und Form
Atelier Schiemann, Ruhrgebiet und Umgebung
Beatles Museum
Berlin Bleibt Bunt
Cityproducts
Danacards
Duckomenta
Düsseldorf Shop
Fink Verlag
Gutsch Verlag
Happy Postcards
Inkognito
Kartenküche
Kochformel
Loyal Plush
Papersisters
Penn un Tint
PostcardAdventure.eu
Postkartenshop Berlin
Pummel and Friends
Skowronski & Koch Verlag
Stayinspired.de
Greece 
Anamnesia
I love Thessaloniki
Neanikon
Ploos Design
Thiki
Hungary 
India 
Auroville
ATLASkeeda
Destino
Dolls of India
e Post Office
Gandhi Ashram
Itokri
Kultureshop
Mario Miranda
Postcardbazaar
Postcards ville
Postjunction
Read Bengali Books
Shop Clues
Ireland 
Badger & Blue
Penpaling Paula - Illustrated postcards and all kind of stationery
Real Ireland
Soul Links Postcards
The Wild Postcard Project
Netherlands 
Alternote
Amsterdam postcards
Artunlimited
By Kris
By Zenz
De Blauwe Maan
Decartograaf
DewyCreations
Dieren kaarten
Dille & Kamille
Elpapel.nl
Envycards
Essencio.nl
Fairyland
Goedkope ansichtkaarten
Happy postcrossing
Hip en stip
Hollandsekaart.nl
Leuke post
Muller wenskaarten
Mymagicards
Natuurlijke foto
Post & Papier
Postcards from Essie
Postzegel erop
Stationery heaven
Stationery world
Tinstarcompany
1001 kleuren.com
Latvia 
Lithuania 
Agapics
Favorite Postcard
MonaiLT - Etsy
Nieko Rimto
Norway
Philippines 
Cynthia Bauzon-Arre
Papemelroti
Pinspired
Poland 
Delicious Postcards
House of Postcards
Napiszkartkę.pl
Postallove
Postrabbit
PostcardShop
1001 pocztówek
Portugal 
Romania 
Russia 
Amelie-cards
Сardamon
Сards shop
Darlingdove
Dreamcards
Еdencards
Giraffepostcards
Grape art
Kartinka24
Lovelycards
Maria Biktimirova
Мeleniza postcard
Moonpost
Мypostland
Twinkle card
Марк Штемпель
Орех издательство
Открытки ежика
Postal Shop
PostcardPress
Почтомания
Почтовый переулок
Roman Papsuev
Cтранник
Улиткард
Чердак
WOW-CARDS
ILLUSTORYART
Singapore 
Spain 
Sweden 
Adlibris
Jönköpings läns museum
Kalenderkungen
Kortbutiken
Postmuseum
Tradera
Upside
Switzerland 
AS Verlag
Bildreich
freshfish
Lightmotif Editions
Werd Verlag
The Postcard Society
Schöne Grüsse
Taiwan 
Nisan Design (World Travel Postcards)
Turkey 
a pinch of sketches
İkisatır
Kagito
Kartpostal Kutusu
Lösev
Paper Street Co.
Uranus (Cardbook)
United Kingdom 
Anna Wright
Art on a Postcard- Proceeds donated to The Hepatitis C Trust
British Library
Cardtoons Publications
Cavalier Postcards
The Curious Pancake
Dave Thompson Art
Festival Postcards- Postcards from UK Festivals
Hannah Longmuir
Kettle’s Yard
Lagom Design
Leeds Postcards
Ohh deer
Papio Press
The Postal Adventures of Morris Mouse
The Postcard Store
Post Snail Press
Royal Mail- recent PHQ editions
Salts Mill Shop
Sugar & Sloth
Victoria & Albert Museum
The Wallich - Welsh charity - all proceeds go to help people experiencing homelessness in Wales (currently not taking orders)
The Wooden Postcard Company
Wrendale Designs
Wuzci
Etsy shops
AlexiaClaire
BBIllustration
BonbiForest
BookishlyUK
emilymackenzie
FerneCreative
HandsOffMyDinosaur
KatieAbey
TheLetteringTree
LittlePaisleyDesigns
PrinterJohnson
RaahatIllustration
SophiasIllustration
tilliecm
TomHardwickDraws
ZoeSpryDesign
Cally Jane Studio
Search for more on
ebay - refine search to ‘auction only’ for second hand items
etsy - refine search to ‘UK shops’ for local sellers
notonthehighstreet
USA 
MailByNina - Fun snail mail postcards
Cafepress
Changing World/VisionWorks
Christopher Arndt Postcard Co.
Deviantart
Estate Sales (Usually Vintage)
JetPens
Pike St. Press (Seattle-themed postcards)
Pomegranate
Postcard Fair
Pumpernickel Press
Tom Haseltine Photography
Zazzle
Ebay shops
PostcardsAndMore
Etsy shops
LouPaper
Postcard Fair
Poxodd
MailByNina - Fun snail mail postcards
Olechka Design
Archive Paper and Press
Redbubble shops
Frank Moth
NineRavens
REALDesign
Isabella Marowski
Whole sale
Argonaut
Lantern Press