How do I know if a stamp is real or fake?

The only way to know if a stamp is legitimate is to have it “expertised”. This means you take it to a specialist who will examine the stamp, for a fee, and issue a certificate atesting to whether it is legitimate or not. If you are in any doubt about the legitimacy of a stamp you should do a bit of research and compare it with other similar stamps.

Royal Mail comes to our aid, and gives some advice (for UK stamps):

 

How can I be sure that I'm buying genuine stamps?

1. Genuine stamps will have the following anti-fraud features:
2. Die cuts within the body of the stamps
3. The words 'Royal Mail' printed in a special ink across the surface of the stamp
4. Wider oval perforations along both sides, close to the base of the stamp
5. Books and sheets of stamps will have a secure laminate underprint featuring the words ‘Royal Mail

How can I spot used or counterfeit stamps?

Counterfeit stamps vary in quality and type and may be difficult to identify. Some may have one or more of the following characteristics on our 1st and 2nd Class stamps:

 1. Cost less than the official Royal Mail prices
 2. Security ovals on each side of the stamp are missing or uneven
 3. Unusual colourings
 4. Uneven borders
 5. An unusually shiny surface
 6. Stamps may be stuck on to what appears to be greaseproof paper
 7. Books of stamps with anything other than 6 or 12 stamps included. Royal Mail only sell 1st and 2nd class stamps in books of 6 and 12.

How can I spot used or counterfeit stamps advertised on a website?

It's not possible to tell if stamps are genuine or not from pictures on a website, usually because the stamps displayed might not be those you receive and it's hard to tell from the photos.

There's some interesting information about the history of Stamp Fraud in here as well.