Use websites like Felon Spy to see if you neighbor has been convicted of a crime. Sex offenders lists can also be another resource for checking to see if your neighbor has been convicted of a sex crime. For most of these sites, all you need is a name or an address.
Find a window in your home with a good view of your neighbors' house. A dark room helps you remain out of sight and you may want to stand back from the window as well. Some people like to keep binoculars or a telescope handy. You can also spend a great deal of time outside in the yard close to the neighbors home doing yard work, sunbathing or reading.
Put up cameras around your home. Although it's not wise to point outdoor cameras at your neighbor's home, you can put them around your own home if you suspect that your neighbor is damaging your property or stealing items from around your home.
Talk to other neighbors. You'll be amazed at the information that you can gather from others, without them even realizing it in most cases. Keep the questions discreet unless you know that the other person is suspicious about your neighbor as well.
Take notes on what you hear or see. Notes on your neighbors will help you see patterns and suspicious activities. Use a notebook or type the notes into your computer.