I recently decided to play through the original red again I dug up my ol' kiwi GBC, popped the cart in....removed and blew a cloud of dust out, popped it in again and started reliving the good ol days, and I must say I have really been enjoying it. That little screen with no backlight, that legendary music, those horrifying sprites (Golbat *shudder*) Today I actually went to the store and bought a pack of batteries for something other then a TV remote, and I loved every second of it.
I miss the bicycle music staying active for as long as you were on your bike, not simply until you enter a new area on it.
I miss secret bases.
I miss The ability to use Cut to clear away tall grass
I'm sure there are other things that I miss, but I can't think of them right now.
Oh, I miss Legendary Pokemon being sidequests that you could do when you damn well felt like rather than stuff you HAD to do (the fact that HGSS forces you to fight Ho-Oh and Lugia prior to fighting the elite 4 is the only reason I still prefer Crystal)
Oh, speaking of HGSS, I suppose I can say I miss Pokemon following you around. I hope they bring that back, and I hope they let you choose what Pokemon follows you rather than just making it automatically the first one in your team.
Don't forget to check out my MegaTen themed webcomics at http://www.drunkduck.com/user/Strain42/ (Currently Updating: Persona 4TW Add-On M-F)