Day & night: I honestly thought having time of day and how it affected which wild Pokémon you battled was one of the best features of any Pokémon game.
Female main character: Ok, I never owned Crystal but it made a nice change from having male only characters to pick from.
Apricorns: A feature admittedly I didn't use much, but one that came in very handy.
Breeding: It started in Gen II and set the benchmark for the following games. Excellent addition with a lot of neat features.
Shiny Pokémon: I've only ever caught a paltry 3 or so, but this was the beginning for them and let's face it, if you'd completed the already massive game and completed the normal Pokédex, there was nothing to stop you trying to complete a shinydex.
Pokérus: Godsend to EV trainers everywhere.
The inclusion of Kanto: Not one, but TWO huge worlds to explore plus with a few exclusions (I'm guessing due to size limitations) the Gen II Kanto was more or less completely faithful to the original.
New evolutions: Gen II gave us some kick-ass evolutions (Espeon & Umbreon, anyone?) and also some new ways to evolve your Pokémon, including new stones and items.
Berries & item holding: Arguably one of the best features that came with Gen II, holding berries & items not only effected evolution etc but added a whole new dimension to battling.
Phone calls: Okay, i'm not as big a fan of this one as with the exception of Swarm-watchers I found the constant calls about Hikers battling "tough Starmies" incredibly annoying, but that said it came in handy if ever you needed to level up some lower-level beasts. And along with the SS Aqua, it meant you could rebattle a reasonable selection of trainers over and over.
Steel & Dark Pokémon: Yes.
Icy floors!: Okay, a bit childish but I adored sliding around in Ice Cave XD
Better music: Just my humble opinion, but I thought some of the battle themes (Especially for Champ Lance & your rival) were amazing, and a vast improvement over the Gen I games. Some of the music for the cities was class as well.
Happiness: Might just be me, but I enjoyed making my Pokémon happier by grooming/haircuts etc. Even if it was an expensive task.
Trainer names: A small detail, but it gave your opponents a sense of personality instead of just being some generic grunt
or Cooltrainer.
Better gyms & leaders: Again, just my opinion but I prefer the Gen II gyms & leaders to the ones in Gen I for the most part.
Mystery Gift: Stuff for free! Plus I liked the way you got to battle the person you last Mystery Gifted in Viridian's Trainer House.
There are probably other things but for now that's all I can think of. Some of the things that didn't make GSC so great were Baby Pokémon (un-necessary and a cheap way to bump the Pokémon tally to 251 imo), the TMs available (Some of them sucked and made me wonder why they didn't just keep a few of the Gen I TMs instead) and the overall lack of challenge (Leaders & Leet Four's Pokémon could have done with another few levels added on imo). But the positives vastly outweight the negatives, and that's why Gen II is my fave generation ^^