In a recent post, we presented Rav Ovadyah Yosef's approach to the issue of using romantic melodies for davening.
Now, the rest of the story...
The Tzitz Eliezer (Vol. 13:12) rules that it's forbidden to sing kaddish/kedusha to shirei agavim. He says its a toevah to put divrei kedusha in begadim tzo'im. He says it's a ma'aseh Satan to get people to sing tunes which bring a loss in the purity of one's kavana both knowingly and unknowingly.
He argues that the melody is the essence of the song (re'ach hashir) and many times conveys the meaning independently of the lyrics. He dismisses the argument some make that it won't affect them as "just words". And, he writes, it certainly causes the hamon am to have improper thoughts.
He explains his ruling: The Rif writes that a shat"z who is meranen b'shirei arev (it doesn't have to be during tefilah) is given a warning. If he doesn't stop, he is removed from his position.
he cites the Rema who rules like the Rif. There is a question as to whether the text of the Rema reads "Shirei Agavim" (romantic songs) or "Shirei Nochrim" (secular songs). The Magen Avraham reads "shirei nochrim." The MA quotes the Sefer Chassidim (238) re:teaching a priest and says the Rema is referring to tunes that are used for Avodah Zara.
The Tzitz Eliezer takes issue with this and says that this is not the Rema's reason. Rather, the Rema holds like the Rif that shirei agavim are always assur and the Sefer Chassidim is adding that shirei avodah zara are assur. He then quotes the Sefer Chassidim (768) re: one who has a good voice, and points out that it doesn't say anything about avodah zara there because 9he claims) it refers to shirei agavim.
He brings the Radvaz says that the Rif (when he writes shirei arev) means shirei agavim and since the Rema is based on the Rif... (this works better if you're gores "shirei agavim" in the Rema.)
He argues that even the Bach and Magen Avraham, who interpret the Rema as referring to shirei avodah zara, would agree that shirei agavim are assur. It's a kal vachomer. (This is Rav Waldenberg's interpretation of the Bach. The pashtus is otherwise.)
He brings the Ma'aseh Rokeach says it's assur and may also be a violation of u'vechukoseyhem lo seyleychu.
Ra Waldenberg then points out that although the Chida critiqued the Ma'aseh Rokeach (re: Maharam Lunzano) he didn't take issue with his psak.
He argues that the chachamim who sang nigunei nochrim didn't know the source so it didn't affect them. (I find this assertion hard to believe. Also, it seems to conflict with his idea of the melody being the "re'ach of the song.) He writes that those who know where the melodies come from are affected by them.
He cites Krach Shel Romi and vehemently disagrees.
He brings the Divrei Chayim, who writes about those who use shirei agavim for tefilah: "oy lahem lepsaim halalu areyley lev, eyn tevunah bahem."
The Tzitz Eliezer quotes Shu'T Ziknei Yehuda (R' Yehuda Aryeh of Modena) who praises professional quality singing by chazzanim and say repeating words during tefilah is permissible. He says to ignore him because he was a kofer and a gambler.
This concludes the summary of the Tzitz Eliezer's responsa.
In a related note, the Yosef Ometz (quoted in Minhag Yisroel Torah) says it's forbidden to use secular tunes for davening, and says we shouldn't try to be smart and say that they stole the tunes from us in the times of the Beis Hamikdash. That's an approach I've seen some in the J-blogosphere take and it strains credulity. At any rate, here's a Chassidic source that doesn't accept that approach.