All kids hit, whether you spank your kids or not it doesn't matter, all kids at one point or another in their life are going to hit someone else. Just like all behaviors how you as a parent respond to the hitting will determine how long the "hitting" phase lasts. Typically boys hit way more often than girls because boys are less verbal and more physical, but girls still hit. There is a great article here that talks about how to handle when your kids hit.
To add to the article, I am a firm believer that you do not punish hitting with hitting. When my kids choose to hit other kids then they choose to no longer be able to play with their friends or siblings. Depending on the level of "pain" they inflicted will determine how long they cannot play. Typically I tell them that they cannot play until their friend feels better, so if the hurt kid cries for five solid minutes then my kid will sit out from playing for five solid minutes. I do have my kids tell the friend they are sorry - but sorry is not enough! Too often I have had another kid hit one of my kids and they think that just because they said they were sorry that is enough - likewise with the parents, I have had mom's look at me and say "sorry my kid hit yours" and they think that makes it o.k. Now occasionally it is o.k. if it is a mild hurt - but if your kid hit my kid hard enough to leave a mark, cause them to bleed, or cause other serious injury sorry doesn't cut it.
If my kid makes another kid bleed, they will help clean up the blood and they are done playing and we will leave. If we cannot leave then they will sit on the couch until it is time to leave, because that is serious and kids need to know it is not o.k. to hurt our friends. If it is an accident, i.e. they were both running and ran into each other and the kid fell and got hurt so they are bleeding my kid will sit out until the bleeding is under control.
One thing I disagree with in the article is having the parent apologize for their child - as soon as my kids can talk they are taught to say they are sorry.
What do I do when other parents aren't o.k. with my discipline style? This rarely happens because my kids are disciplined when my kid hurts another kid, but I always talk to the other parent about what happened and we usually come up with something that works for both of us. What do I do when I am not o.k. with another parent's discipline style? It depends on how often my kid is hurt by the other kid, if every time we get together the kid is hurting my kid and the mom does nothing about it, or just makes the kid say sorry and nothing more then we will no longer play with that kid, they will not be welcome at my house and I will not take my kids to their house. Also I do teach my kids to hit back. My kids know that it is not o.k. for them to hit someone, but if someone is hitting you then you have every right to defend yourself and hit back and they will not be punished for that, and when the kids both come crying about what happened ad find out one kid hit and then the other kid hit them back, I just say, "well sounds like you worked it out, next time maybe you could use your words instead of your fists, but if you don't want to get hit then don't hit first."
How do you handle it when kids hurt other kids?