Ateji (当て字) was popularly used before World War II, but after the war use of katakana became more popular and I do not think even schools teach ateji anymore. However, some of examples are:

Asia, アジア, 亜細亜
India, インド, 印度
Philippine, フィリピン, 比律賓
England, イギリス, 英吉利
Holland, オランダ, 和蘭
Paris, パリ, 巴里
Cabbage, キャベツ, 球菜
Coffee, コーヒー, 珈琲 (may still see this at coffee shops or kissaten in Japan.)
Tomato, トマト, 赤茄子
Butter, バター, 牛酪 (may see this on labels on butter)
Beer, ビール, 麦酒 (may see this on labels on beer)
Piano, ピアノ, 洋琴
Glass, ガラス, 硝子

I really do not think even natives Japanese will understand these days if signs were written in Ateji.