It is customary for a Jewish male to be circumcised 8 days after he is born. You can read below to find out what a Rabbi says about circumcision and the practice of baby showers.
Brit Milah is a mitzvah, a commandment of the Torah. On the eighth day, the boy is to enter the covenant that links God and the Jewish people. This rite has been practiced continually since the days of Abraham and Isaac, and is how every male enters the brit, the covenant. Frankly, Jewish men don't seem the worse for the experience.
When a Mohel or person who circumcises, performs the circumcision, the entire procedure can take anywhere from 30 seconds to two minutes. It is quick and the child recovers quickly. A good Mohel performs anywhere from three to ten circumcisions each and every day, developing a specialty and expertise that none can match. A pediatrician, on the other hand, performs a circumcision far less often, and the medical procedure takes a good half-hour, during which time the poor boy is strapped down, unable to move, and has his penis clipped at several places.
I have only been to one medical circumcision, and I will never witness one again. It was horrible.
Most authorities of Jewish law have ruled that it is indeed permissible for a Mohel to administer a local block, and almost all Conservative and Reform mohalim do so as a matter of course. Find a good Mohel in your area, and ask upfront about the possibility of an anesthetic.
Give your child the gift of a brit milah, or ritual circumcision, rather than the questionable medical procedure of a medical circumcision.