Shehecheyanu on a Brit Mila
Although the Rambam and other earlier authorities rule that a father is to recite the "shehecheyanu" blessing at the brit of his son, other authorities disagree and argue that the blessing should be omitted. This dispute has made for the development of different customs between different communities, and most notably, between those who live in Israel and those in the Diaspora.
It actually seems quite logical that the shehecheyanu blessing would be recited at a brit mila. In fact, doing so is consistent with the rule that shehecheyanu is to be recited when performing mitzvot which occur very infrequently. Nevertheless, a number of authorities argue that, although the mitzva of brit mila is undeniably infrequent, it is, however, a mitzva which causes pain to the one upon whom it is being performed. As such, the joy in the performance of this mitzva is somewhat diminished which indeed calls into question the legitimacy of reciting shehecheyanu.
The idea of not reciting the shehecheyanu blessing when a matter involves pain seems to be at odds with the halacha that one is to recite "shehecheyanu" upon the death of one's father. Although the passing of a parent is a saddening and painful experience, the knowledge of one's impending inheritance and enrichment necessitates the recitation of the shehecheyanu. Nevertheless, there is no contradiction between the two cases. This is because at the death of a parent it is the child who is both saddened by the loss as well as delighted by his inheritance. These two emotions are experienced by a single person. At a brit mila however, the aspects of happiness and pain are split between two different people. The baby is in pain from the surgery while it is the father who is happy to be able to fulfill a special mitzva of the Torah. For this reason there are those who feel that shehecheyanu should not be recited at a brit.
The Shulchan Aruch rules that the shehecheyanu blessing is to be recited at a brit mila ceremony and this is the custom in Sefardic communities worldwide and the predominant custom among everyone in Israel. Ashkenazim in the Diaspora generally do not recite shehecheyanu at a brit in accordance with the ruling of the Rema. One should be sure to seek rabbinic guidance regarding whether or not to recite shehecheyanu when making a brit for one's son.
 Rambam, Hilchot Mila 3:3.
 Tosfot, Sukka 46a.
 Mordechai, Shabbat 422.
 Shevet Sofer, YD 30.
 Beit Yosef, YD 265; YD 265:7.
 Rema, YD 265:7.
 Dvar Yehoshua 2:63.