Bless Me for Peace

The Rambam's fifth fundamental principle of Judaism includes that we may only pray to God and to no other being (link). This precludes praying to angels. According to the Rambam, this is tantamount to idolatry. This position was agreed to by other rishonim, such as the Ramban (Kisvei Ha-Ramban, vol. 1 p. 171) and the Sefer Ha-Ikkarim (1:3).

Based on this, the Maharal questioned a passage in selichos called "Makhnisei Rachamim" in which we ask angels to bring our prayers to God. According to the Maharal, this is tantamount to idolatry. The Chasam Sofer (Responsa, Orach Chaim 166) elaborates on this Maharal and says that he personally inconspicuosly skips "Makhnisei Rachamim" for this reason.

This same issue seems to arise in the third stanza of Shalom Aleikhem -- "Bar'khuni Le-Shalom" -- in which we ask angels to bless us. For this reason, the practice in the Volozhiner Yeshiva was to skip the last two stanzas of Shalom Aleikhem. I believe that this is the practice of R. Hershel Schachter and I know that R. Mordechai Willig does this (as do I). (cf. Halakhic Man, p. 44; Nefesh Ha-Rav, pp. 215-216.)

However, the Minchas Elazar (1:68 and in Nimukei Orach Chaim 559:3) strongly defends the practice. Along with talmudic proofs, there are two rishonim -- Shibbolei Ha-Leket no. 282) and Responsa Mahari Bruna (no. 275) -- who explicitly permit this type of practice. The She’arim Metzuyanim ba-Halakhah (128:7) also allows it.

For a broader overview of this topic and a discussion of an eighteenth century debate about this, see this article (PDF) by David Malkiel.