1. There isn't a good reason to do it. I consider the burden of proof to be on those who favor circumcision, because the "default" option is generally inaction. Further down I'll answer the most common "reasons" that people give in favor of circumcision.
2. I am not Jewish. Circumcision was mandated by God as a sign of the covenant -- something that was definitely a sacrifice -- and we are told in the New Testament that it is not necessary. (N.B. Circumcision as practiced before the time of Christ was also much less drastic. Thousands of boys would have died from blood loss and infection if they had been circumcised according to the current method without our current medical care.)
3. The Catholic Church seems to oppose circumcision. For example, from the Council of Florence in 1439: "Therefore it strictly orders all who glory in the name of Christian, not to practise circumcision either before or after baptism, since whether or not they place their hope in it, it cannot possibly be observed without loss of eternal salvation." Besides, the Church teaches the importance of bodily integrity: as long as an organ or body part is functioning properly, it should not be damaged or removed. This is the same as the argument against sterilization. For more, read this article.
4. God does not make mistakes. Every part of the body has a function and a reason for existing. We could all live with one finger cut off, but we don't do it because the finger still has a function. A couple generations ago, children's tonsils were routinely removed because they looked like they might be a problem. Now, we no longer do this, because it's been discovered that tonsils have an immunological role, and it's better to have your tonsils if they are not actually infected. Although people are still puzzling over the role of the appendix (some interesting studies on this have been published, though), we do not proactively remove the appendix. First, it might have some use we don't know about; and second, we do not put people through surgery unless there is a clear benefit to be gained.
5. Circumcision is inhumane. It is normally done on infants without anesthesia. (It is not considered safe to use a general anesthetic, and a local anesthetic is not completely effective and so is not usually used.) The argument against this is, "Well, he won't remember it." I don't think that matters at all. If it did, I wouldn't be so careful with the diaper pins -- because, hey, if I accidentally stab the kid with a pin, it doesn't matter because he won't remember it! Painful experiments on infants are considered unethical. (Sadly, this has not always been the case: extensive experiments have been carried out on infants in the past, to determine whether they could feel pain. The verdict is that they feel pain as intensely or more intensely than adults. But I think it's horrible that they went around poking newborns with pins in order to find this out.)
A few generations ago, "twilight sleep" was a common anesthesia for birth. Women were told that they would sleep through the birth and experience no pain. In fact, they experienced extreme pain and a loss of control -- they just remembered none of it. Women were blindfolded and strapped to beds in order to give birth. Later this, too, began to be considered unethical.
6. I don't believe I have the right to make this decision for my son. As I pondered the question, I realized that I have no idea what he might want when he is older. I know circumcised and intact men who are happy with the choice their parents made for them. But my son might not be. Whichever decision I made for him, he might want me to have made the other one. However, if I had him circumcised, he would not be able to undo it. If I left him as he is, he could have it done later if he wanted. So I picked the option that he would be able to change later. (Circumcision is less painful when done on adults, because they can be anesthetized, and also because the foreskin has retracted and doesn't have to be peeled off.)
7. Circumcision is considered by the American Medical Association and the American Academy of Pediatrics to be non-therapeutic. Neither association -- in fact, no accepted medical association -- recommends the procedure. Instead, they say it is a matter of personal choice, with no medical reason to recommend it.
8. Circumcision removes around 20,000 nerve endings in a very sensitive place. If my son gets married, he might want those later. The foreskin also has a protective role. It's not a worthless bit of skin, but a complex and useful mucous membrane. (This link has more, but there's one picture which women might want to avoid looking at. Sorry about that.)
9. 89% of women who have experienced both prefer an uncircumcised partner, according to one study.
10. Circumcision of an infant can result in serious injury, infection, or hemorrhage -- which may lead to death. It only takes 2 ounces of blood loss for a newborn to bleed to death -- an amount easily absorbed and hidden by a diaper. There are a lot of blood vessels in this area, and all it takes is for a clamp to slip or an artery to reopen to begin a hemorrhage. Children of both sexes under the age of 10 are more likely to die from male infant circumcision than from choking. I don't give my baby tiny toys he could choke on; I'm certainly not going to risk his life voluntarily. More on the risks of circumcision.
11. Circumcision interferes with breastfeeding. (And you all know how I feel about that!) Frequently an infant who was nursing well before circumcision will come back glassy-eyed and unresponsive. They often fall into a coma-like sleep with no REM (which is not natural or healthy for an infant anyway) and can't be awakened to nurse. When I told the lactation consultant that my baby was not going to be circumcised, she breathed a huge sigh of relief. Apparently she has a very hard time getting breastfeeding established with a circumcised infant.
And a response to the supposed benefits of circumcision:
1. Circumcision was popularized as a way to discourage masturbation. In fact it has the opposite effect, by a large margin.
2. Circumcision is supposed to prevent urinary tract infections (UTIs). In fact, the foreskin has a protective effect against UTIs except in the first year of life. At that time UTIs are slightly more common in intact infant boys, but the difference (1.26%) is not statistically significant. Also, breastfed infants only have 38% of the UTIs of formula-fed infants. So, if you want to protect your son from UTIs, breastfeeding is a much more effective route. Also, girls are at least four times more likely to get a UTI than boys (intact or circumcised). Yet circumcision of girls -- a very similar procedure -- is not commonly done in this country. In fact, it is illegal. UTIs can be easily treated with a course of antibiotics or even a jug of cranberry juice. It is not an infection which requires surgery to cure or prevent.
3. Circumcision does not prevent STDs. One, rather unscientific study in Africa showed male-to-female transmission of HIV was somewhat reduced if the men were circumcised. (Note: a commenter informs me that subsequent studies said the opposite.) However, transmission of gonorrhea and clamydia seems to increase in circumcised populations. Europeans aren't known for being more moral than Americans, just less likely to be circumcised, but their rates of STDs are much lower. In any event, I doubt any sex-ed teacher is ever going to say, "Circumcised boys are protected from STDs, so you can ignore all this and go sleep around without a condom!" No, risky sex is risky sex, and no one should get a false sense of security just because they are circumcised.
4. Intact boys aren't at much risk of getting teased or looking different, because infant circumcision rates in American have now dropped below 50%.
5. Hygiene for an intact boy is quite simple. Before natural retraction (which happens at an average of 10 years old) nothing need be done; afterward the boy can retract his foreskin and rinse with water. That's it. If the parents are embarrassed to explain this to him, they can get him a book on hygiene which will let him know. There are many much easier ways to deal with this issue than cutting off a bodily organ.
6. Some people circumcise their sons "so it won't have to be done later." In fact, 10% of boys circumcised as infants will have to have their circumcision re-done later. 1% of intact boys will be told (rightly or wrongly) that they need to be circumcised later due to a medical condition. So, you have a better chance of avoiding unneeded surgery by never getting it done in the first place. (Source.)
That's all I have to say on the topic. I have avoided graphic descriptions of what is done in a circumcision because I wanted to work your reason rather than your emotions, and the details are frankly horrifying. A video would be more shocking still -- many nurses refuse to participate in circumcisions after having seen one, because they are convinced of its cruelty. If you're considering circumcising your child, I would encourage watching such a video before making up your mind... if you don't have the strength to watch it, how could you force your child to undergo it? But for those who do not plan to circumcise or do not have children, I wouldn't advise watching those videos, because they are rather intense. (I did not watch the videos because the descriptions alone brought me near to tears.)
Feel free to share this post however you like -- I tried to gather the reasons I found the most cogent to save people the trouble of tracking down all the facts themselves, as I did.