Okay, here we go, can of worms time
I'm currently running a rear projection crt so some of the benefits may not be as applicable to direct views.
Near perfect black level with no dithering
Pixel spacing (probably not as applicable for direct view)
Free antialiasing (reduction of stair step affect due to rounded vs square pixels)
Very little input lag when properly set up with analog signals (mine currently isn't
Fast pixel response
Refresh rate contributes to excellent motion performance as well.
Multisync resolution capability (The best crt's hit 1080p and possibly beyond)
Minimal phosphor lag
Shadow detail (can be compensated for with specific gamma related equipment)
Flicker (high end crt projectors don't have as much of an issue with that because they allow higher refresh rates)
Resolution is usually lower.
size (some nice crt front projectors out there though)
Support of modern inputs.
Viewing angle (rear pro, though my 2002 exceeded my expectations by a fair margin)
I'm not to sure about color quality as each display tech has a different way of going about it... but i certianly don't have a crt so i can play my retro light gun games
emulators and modern peripherals would have me covered if i was up for a game of Duck Hunt