Please don't deny your children a passport based on military service. I and my children have French and American citizenships.
1. Things can change. In our case, the military service stopped before I had my son.
2. Even if military service is required, in the case with France, they used to get a letter on their 18th birthday. They simply said, yes, I'll do it or no, I'll renounce my French nationality. No big deal. Let your child make this decision at the time. He'll (assuming it's a guy) will have documentation that he renounced his other citizenship instead of telling passport control simply that his parents never bothered to get him his other citizenship.
3. Sometimes there are ways around it and exceptions are not unheard of. I had a coworker, also French and American and over age 18. I was curious as I knew he grew up in the States. Turns out, when he joined the American military (voluntarily, not specifically for this reason) the two countries had an agreement and his American service counted. He got to keep both citizenships.
In some cases (Israel, just to give an example) if the young person is living elsewhere at certain times of their life (established resident, not a well-timed vacation or study abroad deal!), they can get an exemption. Some countries too offer non-military alternatives for non-residents. A deferment might also be possible.
So go ahead and do it, since you never know what the future may bring and you want to keep as many doors open for your child's future as possible. You still have many years to get the information your child will need.
I want to add that in some countries, if the parents are not the nationality of the child's birth, citizenship can hinge on what kind of education they opt for him or her. Here in France, for example, your child doesn't necessarily have to be in public school but if you opt for private, the child has to be following the French education system. If you put him or her in say, a British or American school, you may be limiting their citizen options in the future. I believe Italy has similar rules.
I have to say that getting my French nationality was almost as easy as renewing my 10 year residency. I don't think this is haphazard. I think they want spouses to become citizens.
Also, don't panic about the paperwork. They asked for my father's birth certificate. Turns out there were a few errors in it and when I contacted the whatevers in Pennslyvannia to get some sort of correction, they said my father would have to do it himself. Then when I told them there was a slight glitch (my father died in 1974) the procedure involved going to court in California (where he died and where I'm actually from...), getting everythings documented, etc. I called the courthouse here in France and gave them my little dramatic story, to which they said they would accept just my mother's and their marriage certificate.
The consulate can also do a little "swearing ceremony" in lieu of your FBI police records. Some accept this, some don't but it is easier than having to prove you don't have a police record back in the U.S.
Hope that helps any of you living elsewhere if you have the opportunity to get another citizenship!