We hear all the time that victims have turned their information over to the police and they don't want to report here or on other ant-scam sites, because their report is under investigation. This is frustrating for us because we know that the report will go nowhere. Even the FBI, CIA, MI5 or IC3 (Internet Crime Complaint Center), can't do anything for you. That doesn't mean that you shouldn't report to these agencies, but THIS SITE and others like it, are the only places where you can anonymously report your scammer and expose him to potentially save others from his scam. This is the only way you can do any real damage to this criminal's nasty business.
That said, if you just got your heart broken or didn't lose anything of value, it's a waste of time and your law enforcement resources to ask them to chase a scammer who is in another part of the world. They simply cannot cross their boundaries of jurisdiction. But if you lost money, then you should call your local police. First if you have homeowners insurance and on the very slim chance they'll cover your loss, then you'll need a police report. Secondly, scammers are adept at identity theft. Again, you may have insurance to protect you from identity theft, but you're always going to have to start with a police report. Last, if you received gifts, forwarded anything to the scammer like merchandise or checks, or even just letters he asked you to send to others, you are at the end of the paper trail of those items. If there is any chance the police might show up on your doorstep asking questions, it is always best that YOU go to them first.
The next best place to go to report your scammer, if you're an American, is to IC3
http://www.ic3.gov/default.aspx. There really is nothing that they will do. They might not even respond to your complaint, but you will be counted as a statistic, which IS very important in fighting these crimes. Please help get the politicians to notice the millions of American dollars that are being siphoned off to Africa. We can always hope for political pressure to get foreign countries to stop the scammers.
Another slightly related topic is the matter of taxes. Often people ask if they can claim the money lost on their federal income tax. The answer is, probably yes, but a few things have to be in place; first, the police report, second your insurance claims denial. Then you have to itemize (long form, schedule C), so if you're a short form filer with no deductions other than dependents, then you won't be able to write off your loss. If you file Schedule C, then I believe the deduction you want is Theft By Deception. However this will never mean you get your money back. All this does is exempt the amount you lost from your already taxable income. In some cases this might result in a larger tax return if your employer has withheld taxes from your paycheck.
Bottom line is, if you sent your money to a scammer. It's not ever coming back. Sorry.