Most foreign countries in
Japanese are written in
katakana, but many have
kanji transliterations dating back to the
Meiji era and before. The use of kanji in this way is dying out: you're most likely to see these transliterations in compound words, like
日米 Nichi-Bei "US-Japan," or
日中韓 Nit-Chu-Kan "
CJK." Where possible (i.e. where I can figure it out), I've noted which kanji pops up in compounds.
Argentina: 亜爾然丁 Aruzenchin.
Australia: 濠太剌利 Osutoraria is the old ateji for Australia. Nowadays you might see 濠洲 Goshu or simply the first character, Go, used to refer to the Land of Oz, especially in newspapers.
Belgium: 白耳義 Berugi.
Brazil: 伯剌西爾 Burajiru.
Cambodia: 柬蒲寨 Kanbojia.
Canada: 加奈陀 Kanada.
China: 中華人民共和国 Chuka Jimmin Kyowakoku is the official Japanese gloss of "People's Republic of China," while 中華民国 Chuka Minkoku is used for "Republic of China." 中華 Chuka and 中国 Chugoku are also used in conversation and writing to refer to China. 唐 Kara is the old Japanese term for China, and 漢 Kan refers to the Han dynasty (and is one of the roots of the word kanji itself). Because kanji are derived from the hanzi used in China, virtually all Chinese place names are written in kanji: 天安門 for Tiananmen, 台湾 for Taiwan, 香港 for Hong Kong, etc. You may see Beijing written as ペキン rather than 北京, but kanji are far more popular than katakana when discussing Chinese places.
Chile: 智利 Chiri.
Denmark: 丁抹 Denma'aku. (insert shoutout to liveforever here)
Egypt: 埃及 Ejiputo... meaning "of dust."
Finland: 芬蘭 Funran, literally "perfume orchid." (thanks to gn0sis for pointing this one out)
France: 仏蘭西 Furansu. It is more common now to use the first character, Futsu, by itself to refer to France. (This can be confusing, because if the same character is pronounced Butsu, it means "Buddha." cf. Namu Amida Butsu.)
Germany: 独 or Doku is used. It literally means "alone." 独逸 Doitsu is an old ateji translation of the native name Deutschland, and is the most common name for Germany in conversation.
Greece: 希臘 Girisha, or the Gi by itself.
India: 印度 Indo, or just the first character In.
Ireland: 愛蘭 Airan. I found this in the big version of Nelson's and never forgot it: it literally translates to "orchid of love."
Israel: Not old enough to earn a kanji, but there is 猶太 Yudaya for "Judea." It literally means "still fat." Makes you wonder...
Italy: 伊太利 Itarii, or the first kanji I when used in compounds. Note that Itaria is more commonly used in conversation.
Japan: 日本 Nippon or Nihon are the two modern use names, and 日本国 Nipponkoku is the country's official name. All of these roughly translate to "Land of the Rising Sun." 倭 and 和, both Wa, are often used to refer to ancient Japan, as is 大和 Yamato.
Korea: 大韓民国 Daikan Minkoku (from the Korean Taehan Minguk) is the official name of the Republic of Korea, aka South Korea. It can be abbreviated 韓国 Kankoku. 朝鮮民主主義人民共和国 Chosen Minshushugi Jimmin Kyowakoku is the official name of the Democratic People's Republic of Korea, aka North Korea. 朝鮮 Chosen (from the Korean Choson) is the traditional Japanese name for the peninsula, but because it is used primarily by the North nowadays, some people think it isn't politically correct. Korean place names can be written in either kanji or katakana: both methods seem to be equally prevalent, so you can write Seoul as either ソウル or 漢陽, and Pyongyang as either ピョンヤン or 平壌.
Malaysia: 馬来西亜 Maraishia (thanks to gn0sis for this one, too)
Mexico: 墨西哥 Mekishiko.
Mongolia: 蒙古 Moko.
Netherlands: 和蘭陀 Oranda, from the name Holland. The middle character ran, which literally means orchid, is used in compounds referring to the country, such as 蘭学 rangaku "Dutch studies."
New Zealand: 新西蘭 Nyujirando. This is an interesting one: the first kanji is the kanji for "new," usually pronounced shin.
Peru: 秘露 Peru
Philippines: 比律賓 Hirippin, or the first kanji Hi.
Russia: 露国 or 魯国 Rokoku: the first one is far more common today. The Soviet Union was called ソビエト連邦 Sobieto Renpo or just ソ連 Soren. The kanji 蘇
So is occassionally found referring to the Soviet Union. 露西亜 Roshia is the common use name for Russia. (Also note that 樺太, Karafuto, is the preferred Japanese spelling of the Russian island of Sakhalin.)
Singapore: 新加坡 Shingapa, or Shingapôru in conversation. (thanks, gn0sis)
South Africa: 南阿弗利加 Nanafurika.
Spain: 西班牙 Supein, or more commonly the first character, Sei, which means "west."
Sweden: 瑞典 Suiden. Called Sueden in conversation.
Thailand: 泰 Tai. Also called Tai in conversation.
Turkey: 土耳古 Toruko.
United States: 米国 Beikoku is almost as common as the katakana transliteration アメリカ Amerika, especially in newspapers. The name "United States" is translated 合衆国 Gasshukoku, but rarely found by itself, outside of translations of American government publications (U.S. Customs forms and the like). You're more likely to see it used as part of アメリカ合衆国 Amerika Gasshukoku "United States of America." 亜米利加 Amerika is the old kanji transliteration. Old kanji names for American cities include 桑港 Soko "San Francisco" (lit "mulberry port"), 紐育
Nyuyoku "New York," and 華府 Kafu "Washington" (lit "flowering government," and also Harvard's name in Chinese: thanks to gak for that tidbit). 加州 Kashû is sometimes used for "California."
United Kingdom: グレートブリテン及び北部アイルランド連合王国 Gureto Buriten oyobi Hokubu Airurando Rengo Ôkoku is the official gloss of United Kingdom of Great Britain and Northern Ireland, but you're more likely to see 英国 Eikoku used to refer to Britain. The ei part comes from 英吉利 Igirisu, which is derived from the name "England," although nowadays it is usually used in referring to Britain as a whole. London, by the way, has been written in kanji two different ways (this is ancient stuff): 英京 Eikyo or "British Capital," and 倫敦 Rondon.
Vietnam: 越南 Betonamu. The more common usage is the first character, pronounced Etsu. Vietnamese place names are always written in katakana.
...and by now you're asking "Where did you get all these from?" EDICT, my children, is the answer.