1.) Is there a service to check the crime rate in a neighborhood?
2.) How can you check to make sure that a home is not built on some toxic dump or that the water in the area is not overly toxic?
1. When you say "neighborhood" do you literally mean some small neighborhood in a particular city, or do you mean a larger area, like a city or zip code area? If the former, you should probably be talking to the local police department for such focused statistics. If you're talking about the latter, there are all kinds of excellent sites on the web, such as the one in the link below, which breaks it down as small as by zip code.
2. As for environmental concerns, you should contact your local or State environmental organization. They should be able to tell you if there are any problem waste sites in your area, or maybe even if the zoning in a particular area ever allowed commercial or industrial use. But there is no way to guarantee that a particular home site is absolutely safe as there are many contaminated sites yet to be documented. Further, there is no way anyone can guarantee that the house was never used as a meth lab, or that there isn't a buried, leaking oil tank underground, etc. You can also get water analyses from your local water utility if you are on city water, or maybe from the local health department if you're not. Beyond that, your only recourse is to spend 1000's of dollars on water and soil testing.
Here is a link that might be useful: City Data
1. I meant like a zip code.
The chief of police can tell you how crime statistics are reported and where you can get them. I don't know if it is broken down to the level of zip code.
It's a good idea to do the environmental check -- I owned a house in Northeast Minneapolis that was near an old factory that produced vermiculite. They let the neighborhood kids play in the piles of vermiculite and people used the stuff to pave their driveways and edge their gardens decades ago. It turns out the stuff was full of asbestos. I had several testings done and none was found in my yard, but who knows. It was a big deal for a while, about 5 years ago, but anyone buying in that area now would never hear about it unless they did their own environmental research. Good luck to you!