As a first time mom-to-be I've had some fears about the public school system, even though I attended public school from kindergarten through high school.
But I get a lot of reassurance from experienced moms. The best advice I've been given is to be involved! Especially volunteering in the class when available, visiting your child at school, helping with school activities, etc etc. When the teacher(s) and administration see you and know you they're more likely to keep you in the loop and, according to one mom, even treat your child better than those who's parents are not involved.
I worked in an public school setting for the last twelve years and I believe that the elementary schools that I have been at are safe and promote learning more so then other options available to my children. I recommend that you do your research on the schools in your area to see how safe they are. There are a lot of options available to you besides a public school. There are private schools, charter schools, virtual schools and home schooling for you to choose from. I explore each of these options in detail on my website at parentsharing.org.
Once you have chosen a school setting for your child, I agree that it is a great idea to stay involved at the school. Not only to make sure that the school is a safe environment, but also to send the message to your child that their education is very important to you.
I wouldn't approach the question by thinking about public schools or public school safety in general. You have to look at the specific public - and alternative - schools that are available to you. Just because a public school a few towns over has a reputation for being unsafe, that shouldn't impact your decision to send your kids to the very safe public school in your town (and vice versa, if you live where the school is unsafe).
But, to echo the other folks, you have to be involved in your kids' education, no matter what school they attend. If they get the signal from you that education isn't important to you, then it won't be important to them.