Removing files from & repackaging CyanogenMod ROM zip files
There are multiple solutions available:
Re-Zip the Image
Advantage: You do it once, and can use the resulting image for multiple devices. That's what I did with CM7.2 for my Milestone 2. Easy enough to do:

create a temporary (empty) folder
unzip the zip file to it
remove unwanted *.apk files from /system/apps (be careful of what you remove, of course)
zip up the directory contents again

Using a graphical ZIP manager (like WinZip or the like), steps would be even easier:

open the zip file with the archive manager
remove the unwanted .apk files
if the ZIP manager requires it, save the manipulated zip

Manually cleanup after flashing, using the shell
This is what ce4 recommended in the comments. It requires you using a terminal emulator on your device:

Flash the image as-is
remove superfluous stuff from the system partition by hand (like rm /system/big/junk/example.mp4)

Manually cleanup after flashing, using other tools
Almost the same as the previous method, but a bit more user-friendly. Disadvantage: this won't do for superflous ringtones and the like:

Flash the image as-is
Use a tool like Titanium Backup or Root Uninstaller to remove unwanted system apps