The queen in Estonian (lipp) is a flag. Arabic (wäziir, firzān), Russian (ferz'), Farsi (vazir, farzin), Uzbek (farzin), Hindi (farzī, wazīr) and Turkish (vezir) among others still use the ancient word of no gender firz for today's chess queen.
REFERENCES
http://www.chess.com/forum/view/general/what-is-the-name-of--this-piece
http://www.geocities.com/timessquare/metro/9154/nap-pieces.htm
http://www.listofchesspieces.com/
http://everything2.com/e2node/Chess%2520pieces%2520in%2520other%2520languages
I can only speak for German and Scandinavian, but, in contrast to English, the names of the following pieces are:
Knight: German = Springer "jumper"; Swedish = springare "jumper"
Bishop: German = Läufer "runner"; Swedish = löpare "runner"
Pawn: German = Bauer "farmer, peasant"; Swedish = bonde "farmer, peasant"
Queen: German = Dame "lady"; Swedish = dam "lady"
Rook: German = Turm "tower"; Swedish = torn "tower"
As you can see, Scandinavian (here represented by Swedish) tends to follow the German model, rather than the English-language one.
It's interesting how the various pieces have been named and conceptualized in different languages. Germans (and slightly later presumably Scandinavian speakers, probably mediated via German) must when the game arrived on their shores have seen the pieces of the newly introduced game and associated them with different things than did speakers of English. So the knight was not a horseman but a "jumper", and the bishop was not a man of the cloth but a "runner". Pawn and Bauer/bonde have some overlap but are still distinct conceptual entities. Even the Queen is known as a "lady" (and not Königin/drottning, as one might expect).
In French, the bishop is neither a bishop or a runner but a "fou" (fool/jester). French pion matches pawn pretty closely.
In English, we don't speak of a "tower" as Germans and Scandinavians do (although the old-fashioned term "castle" persists among the older generations), but of a "rook" which has no etymological value in English as it is originally a loanword from Persian (meaning "chariot"), via Arabic and French. Rook then really points to the Oriental origins of chess, while medieval northern Europeans put their own interpretations on the other pieces, effectively naturalizing them. Not surprisingly we don't find any elephants in the European chess sets.
Can anyone cite examples of differences for other languages? What about Russian, where chess is considered a national game (or even *the* national game?)?