I personally remember getting Pokemon Silver way back when. Unfortunately, earlier this year I tried to load my game...and realized my battery had died. I went ahead and replaced it, but I miss some of the pokemon I had (my Chikorita and my first shiny pokemon, a Spearow, rank up there!)
I just loved so much about it. The fact that it had a real post Elite-4 game in it (which kinda was needed based on how short Johto was), and the fact that I got to face Red was awesome! I hate how in the new games you are limited back to 8 gyms agian...I liked having more "boss" level opponents...which is why I enjoy the remakes even more, since they added all the features missing from GSC Kanto back in (Seafoam Island, Safari Zone, legendary birds, full gyms for Blue and Blaine).
One thing I enjoy more about GSC than HGSS though is the simplicity. I mean, training pokemon was much simpler in Gen I/II than with the current EV system. No worrying about battling the wrong type of pokemon, etc. And the Box cloning trick was mad easy (let me give out shiny spearows to my friends, which helped me get good trades since none of them found anything shiny besides the Gyarados).
I still actually remember my (admittedly nooby) team that I used: A Meganium, the Red Gyarados, a Magmar, the shiny Fearow, Ampharos, and Graveler/Golem. I miss them =(