Selichot - Machnisei Rachamim
At the conclusion of the selichot prayers that are recited during the month of Elul, and in most communities right through to Yom Kippur, there is a prayer which begins with the words "Machnisei Rachamim" ("Those who deliver the prayers"). Machnisei Rachamim is essentially an appeal to the angels that they assist us by personally presenting our prayers and supplications before God. Although this prayer is nearly universal, it is not without controversy, as we will see.
Historically, a number of authorities have been opposed to the recitation of the Machnisei Rachamim section of selichot, arguing that it is forbidden to address any being in prayer other than God. In fact, God Himself seems to say so. As the Talmud teaches: "If troubles come upon a person, do not entreat the angel Michael or the angel Gabriel. Rather, entreat Me alone and I will help you immediately." Indeed, it is noted that one of the principles of faith, as codified by the Rambam, explicitly opposes the practice. As the Rambam writes: "It is only fitting to pray to God and it is not fitting to pray to any other." Those who deny or violate the Rambam's principles of faith are labeled as heretics by most authorities. Similarly, the Ramban rules that anyone who believes that the angels have any special abilities or can serve as intermediaries are considered to be practicing idolatry. As such, a number of sages throughout the ages have suggested alternative wordings for Machnisei Rachamim or have omitted it entirely.
Nevertheless, most authorities justify the recitation of Machnisei Rachamim explaining that the prohibition to appeal to intermediaries only applies when one relies upon them to answer one's prayers. If, however, one is merely soliciting their support, as is the case regarding Machnisei Rachamim, then it is permitted. In fact, the Midrash explicitly teaches that it is a legitimate Jewish practice to solicit the assistance of Heavenly beings in order to better one's chances of having one's prayers answered. Furthermore, we are actually encouraged to always pray in a language that the angels understand so that they might hear our prayers and be moved to advocate on our behalf. It is also noted that Yaakov Avinu himself addressed the angels in prayer with his famous "Hamalach Hagoel Oti" supplication which asks the angels to watch over our children.
Somewhat related to the controversial practice of addressing angels in prayer is that of praying at the tombs of righteous individuals. While spying out the Land of Israel, Kalev made a stop in Hebron in order to pray at the tombs of the patriarchs that he be saved from falling prey to the ten evil spies who were planning to slander the Land of Israel. The practice of praying at gravesites is seen by some authorities as a possible violation of the prohibition of "one who consults the dead". Nevertheless, halachic authorities exclude prayer at a graveside from this prohibition citing Kalev's precedent as evidence. It goes without saying, however, that one is not permitted to pray to the deceased or otherwise ask them to personally fulfill one's requests. Such expressions must be directed exclusively to God.
 Netivot Olam, Avoda Chapter 12.
 Yerushalmi, Berachot 9:1.
 Ramban, Parhsat Yitro.
 Netivot Olam, Avoda Chapter 12
 Chatam Sofer, OC 166.
 Shir Hashirim Rabba to 2:7; Shibolei Haleket 282.
 Shabbat 12b; OC 101:4.
 Devarim 18:11.
 Shach, YD 179:15; Bach, YD 217.
 For a dissenting view see: Sefer Chassidim 450, Darkei Teshuva, YD 179:36; Minchat Elazar 1:68