R/B/Y (and to a lesser extent GSC) really do make the expression "ignorance is bliss" ring true. In those days, knowing the type advantages was enough to make you a badass battler. I sure thought I was hot shit because I knew Ground beat Electric and all that. No EV's or natures to worry about, either... No breeding either. You damn well went out and caught your Pokemon the hard way if you wanted multiples.
More than anything, I miss having only 5 HM's. They each actually had a use. Now they've tacked on stupid crap like Rock Climb... HM's really make playthroughs a lot less enjoyable for me on the more recent games. When you have to waste like every moveslot on your water-type for Surf, Waterfall, Whirpool, Dive, etc., it quickly feels like you can't choose how to play the game. Back in RBY, you didn't even necessarily need a water.
I miss the rival, of course, but I also enjoyed the one in GSC. The RSE one was crap, and DPPt just felt like a watered down Gary/Blue/Green/whatever you want to call him.
I miss not knowing which Pokemon were good other than legendaries and like Dragonite. I still remember going in to the Elite Four the first time with my Nidoking, Nidoqueen, Gyarados, Venusaur, and something like a Clefable and Omastar. I don't think a single one was above 40 and I taught them the most random things.
On a more personal note, I miss the weird nicknames only my 6-8 year old self could invent. My Clefable was called PkMn(the symbols, not letters)RQ and then a male sign on the end or something. I remember my Bulbasaur was named SEE because I tried to name it SEED but missed the D. Didn't even bother changing it at the name rater.
I miss there being a definitive best Pokemon, head and shoulders above the rest. There was simplicity and mystery with the legendaries; the birds just existed, without any explanation. Mewtwo had a semblance of a backstory with the mansion, but it was so vague it only made him more menacing. Seeing the ruins of the mansion... Back then legendaries did things. None of this recent "almost" destroying the world but not actually doing anything.
I could go on for several pages, haha, but I'll quit while I'm ahead.