Dative case works with questions "to whom/to what (they serve)", which is what we have here.
Рыцари служат (кому?) королеве.
If we had to translate a sentence like "The knights carry a queen", we would use accusative case, since the question would be "whom/what (they carry)":
Рыцари несут (кого?) королеву.
Thanks, OlegK. Yes, I saw that рыцарь comes from Middle High German Ritter, originally borrowed from Old French chevalier, something like "rider at arms." But for царь the etymology given is Old East Slavic цьсарь, which originally derives from Latin Caesar. I see also that царь or цар means "king" or "emperor" in several other Slavic languages, all stemming from the same Old Church Slavonic or proto-Slavic root (цѣсарь and *cĕsarjь, respectively), again going back to Caesar.
From this, it would seem that the two have completely different etymologies, and yet, with such similar spelling and closely related meaning (since the knights served the king - or queen! - in medieval times), it seems almost impossible that they wouldn't be related in some way. Can you tell me some more about this influence you mention?
The influence is purely phonetic. There are many examples in most languages around the world when a loan word gets modified to sound more pleasant/familiar . In this particular case, the word first came to Polish and became rycerz (рыцерж in Russian phonetic representation). Since there was already the similar-sounding word "царь" in Russian, this Polish word was modified by the Russian speakers to sound more familiar and thus became рыцарь.
Ah, I see! I saw something about it coming from the Polish when I looked it up on Wikipedia, but I didn't entirely understand how that fit in. I guess it makes sense geographically, in terms of an eastward spread of ideas and culture from Europe in the days when news was carried on horseback. :-) And then Russian speakers incorporated it as a similar-sounding word that already existed in the language.
Спасибо, Олег! Мне очень интересуют этимология и история языков. Дала вам лингот.