Most countries around the world actually have a kanji name. However in modern usage katakana is almost always used instead. But since I have created other totally useless pages, I thought adding one more won't hurt too much...
Here are a few countries that have kanji chosen to fit the pronunciation. These are normally written in Katakana, but occationally, you may find them written:
亜米利加 アメリカ - amerika - America
阿弗利加 アフリカ - afurika - Africa
亜細亜 アジア - ajia - Asia
加奈陀 カナダ - kanada - Canada
印度 インド - indo - India
倫敦 ロンドン - rondon - London
墨西哥 メキシコ - mekishiko - Mexico
巴里 パリ - pari - Paris
羅馬 ローマ - ro-ma - Rome
露西亜 ロシア -roshia - Russia
比律賓 Firipin - the Philippines (added by user in the comments)
仏蘭西 Furansu - France
Here are a few locations in kanji that are used today instead of katakana
大西洋 - たいせいよう - taiseiyou - Atlantic Ocean
太平洋 - たいへいよう - taiheiyou - Pacific Ocean
米国 - べいこく - beikoku - United States
英国 - えいこく - eikoku - United Kingdom
中東 - ちゅうとう - chuutou - Middle East