It is 100% legal in the United States to purchase, own and operate a scanner radio with a very few minor exceptions. We note that because radio law sometimes, but extremely rarely, changes, and because we are not attorneys, you should check your state, local and federal laws if you have any concerns.
There are a few states that have laws on the books regarding the use of scanners in motor vehicles. Kentucky, Indiana, New York and Florida come to mind. There are a few additional states where it's illegal to use a scanner in the furtherance of a crime. Click these links below (which may or may not be up-to-date) for further information:
It is illegal to intercept cordless phone communications (most cordless phones today are spread spectrum and cannot be monitored anyway. It's also illegal to monitor cellular phone conversations and for the last 10+ years the major scanner manufacturers, by federal law, have not produced a scanner capable of monitoring the cell phone band. At any rate, because 99.9% of all cell phone calls now are CDMA, GSM and other highly advanced types of digital (not APCO-25 digital), cell phone calls couldn't be intercepted anyway.
It is also illegal to decrypt encrypted communications. Most public safety communications that use DVP/DES and other types of highly-sophisticated encryption couldn't be decrypted without years of work and a supercomputer anyway. Luckily, relatively few public safety agencies in the U.S. use such systems. In other parts of the world, particularly we know in Europe, the public safety radio systems cannot be monitored.
Scanners are a well regarded and respected tool for the news media, public safety agencies themselves, and for the general public. Americans like to be in the know. They like to be aware of what's going on around them and they like to help the police and fire services whenever possible, by reporting crime, fire, and the like. Knowing what the local authorities are doing and perhaps helping (without interfering -- very important) after having heard something on-the-air, benefits us all.
So scanners are completely legal to own in your home, on your person, and, in almost all states, in your vehicle. They help you build a healthy respect for the job our public servants our doing while at the same time keeping you in the know. Buy a scanner radio today and be informed and enjoy!