Photo by WestportWiki
There are several different ways that you can tell whether a Coach bag is real or fake:
1. The Stitching
One of the reasons that Coach bags are so expensive is because of the quality of their construction. The seams on these bags are always perfectly straight. Each individual stitch should be exactly the same size as the other stitches with no loose, overlapping or crooked stitches.
2. The Coach Creed
Nearly all Coach bags except for very small purses have a small, square leather patch sewn to the inside of the bag that is known as the Coach Creed. On this patch, there is a serial number that follows a very specific format. The basic format looks like this:
The first part of the code before the dash represents the month and year that the bag was made as well as the factory it was made at. The month is indicated by a single letter from A-M (with the exception of I). For instance, January is represented by the letter A, February is represented by B, etc. The next two digits are the last two numbers of the year in which the bag was made. For example, 98 represents 1998, 03 represents 2003, etc. Finally, the last two digits of the first part of the code indicate which factory it was made at. 
The last five digits of the serial number following the dash represent the style number of the bag. A quick way to authenticate a bag is to look up the last five digits of the code online along with the word "Coach". The search should bring up a bunch of other bags that are the exact same style as the bag you are authenticating.
3. The Zipper
The zipper on an authentic Coach bag will be engraved with the letters "YKK".  They may be very small, but if you look closely you should be able to find them.
4. The Pattern
The signature "C" pattern will be on either the inside or the outside of the bag, but never on both. The Cs in the pattern should be facing each other and touching.
Here's a great video that shows you how to spot a real versus fake Coach bag: