Let me know if I missed any!
Asia:
China: dim sum - light dishes served with tea
Japan: izakaya - cooked bar snacks, like tapas, served in an izakaya bar with beer and sochu
Korea: banchan - small dishes of food served with cooked rice
The Philippines: pika-pika and pulutan - little bites of meats and seafood eaten with alcoholic beverages
North America:
Hawaii: pu-pu platter - A variety of hot bites served alongside a small flame for further cooking, and a tropical drink accompaniment
South America:
Argentina: minutas and picadas - small bites served with wine, very much like the tapas of Spain
Europe:
France: hors d'œuvres
Spain: tapas - hot and cold appetizer dishes
Greece: pikilia - a collection of small dishes and dips served with pita bread and ouzo
Russia: zakuski - a variety of small appetizers served with vodka
Italy: antipasti - a variety of items on one plate, either served as a starter before a main course, or is the main course itself
Venice, Italy: ciccetti - small appetizers served with white wine
The Netherlands: voorgerechten - hors d'œuvres-type plates
Germany: vorspeisen - hors d'œuvres-type plates
Scandinavia: smörgåsbord - a collection of hot and cold plates served with slices of dark bread and drunk with aqavit
The Middle East and North Africa:
Middle East/Arabic countries: meze - a collection of finger foods served hot or cold, with an anise-based liquor like arak, or wine
Morocco: kemia - small finger foods
(Images: Demetris Taverna, Create A Cook, La Tombola, Vera Brosgol, Flickr user dane brian, and Flickr user loveu2 - thanks!)






Floral Drink Dispen...

A slightly different beast, perhaps, but when I lived in the Netherlands, I had some spectacular examples of Indonesian rijsttafels (rijsttafelen?), a more-or-less colonialist take on the Indonesian nasi padang. Dozens of small bowls with curries and satays and condiments. Sambal Oelek on everything and several beers to wash it down. Lekker!
India: Thali's.
Mmmm...I adore small bites.
I'm thinking a small bites pot luck party would a great idea!
"Pikilia" (spelled ποικιλία in Greek) is the actual Greek word for "variety" and it's the word the tavernas list in their menus, meaning a plate containing a variety of meze foods. Meze is more like it, as it's used to describe any kind of food that can casually accompany a drink of ouzo or wine.
I also see you list "meze" as used in Middle East/Arabic countries, which may be true, as "meze" is not a Greek word, it's actually of Turkish origins.
I guess that, in terms of food, Greece was greatly influenced by its eastern neighbors.
Indonesian Rijsttafel, very similar to an Indian Thali...
http://en.wikipedia.org/wiki/Rijsttafel