I suspect every language does this to some extent. Some good examples from Japanese:
靴 = shoes 下 = under 靴下 = socks
手 = hand 紙 = paper 手紙 = letter
歯 = teeth 車 = wheel 歯車 = cog / gear
火 = fire 山 = mountain 火山 = volcano
Sadly (?) the Japanese compounds are often only compounds of the symbols, not the spoken words.