Sadly, there is no real good way to prevent decompiling from happening. However, there are ways to protect your files.

Flash Decompilers are tools that reverse-engineer a Flash file from .swf to .fla, which is illegal for users who do not own the file. It will not put the file back together perfectly, but it will do a pretty good job putting things in the right place with the right code.

There are no tools currently available for preventing a decompile of a file completely. So far, there are only tools for preventing code from being imported. SwfEncrypt 4.0 by Amayeta has proven to be a great tool for protecting your Flash code. It will change the code around on import to a decompiler, so that the code will not work correctly. This tool is remarkably useful for game programmers.

If you haven't already, make sure that you Protect from Import your file so that it cannot be easily accessed.

Luckily, most people will decompile a file to view a code for their own project. Since it is possible to protect this information, you can save yourself from these problems.