While .exe files are then most obvious "executable" filetype, there are a whole lot of others.

.bat, .com, .dll, .js, .jsx, etc.

A single pixel in a .jpg file contains enough "bits" to be an executable viral segment that can infect your computer if you view the file. Many email programs block .jpg attachements by default, and require you to override the block to see them.

Office programs that contain macros can execute viral infections. The new formats for Office 2007 should always include an "m" in the four letter file extension in order for a macro to be included, but there's little confirmation that this is a sure-fire way of knowing. (The default "new" Word document is a .docx, while a document that uses any macros should be a .docm. Similarly for .xlsx/.xlsm etc.)

Any file can have more than one "file extension." If you don't set up to always view all of them, what looks like "granny.jpg" could actually be "granny.jpg.exe".

John