>>360140161. Following Pokémon
2. 16 Gyms
3. Best Safari Zone
4. Pokéathlon
5. Gym Leader rematches
6. Elite Four + Champion rematches
7. Pokéwalker
8. GB Sounds
9. Voltorb Flip (actually logic-based, unlike slots, roulette etc.)
10. Battle Frontier (including, over Crystal:)
11. Battle Factory (Emerald, Platinum and HGSS's best feature in my opinion)
12. Battle Arcade
13. Battle Castle
14. Battle Hall
15. Increased levels from GSC
16. Keeps Crystal Suicune stuff
17. Expanded map (Cliff Edge, Seafoam Islands, Cerulean Cave, better Mt. Silver)
18. God-tier soundtrack (and soundfont)
19. Nice tilesets/palettes
20. Good events (Giovanni, Arceus)—they shouldn't have been events though
21. Fixed music over GSC (Upper Goldenrod Tunnel, Executives, Cinnabar Island etc.)
22. Latias/Latios roaming + Kyogre/Groudon/Rayquaza stuff
23. Miscellaneous things (Lance & Clair, Hoenn/Sinnoh Sound, Seals etc.)
24. Shiny Leaves
There, 24 things that make HGSS personally my favourite main series games.
I do admit, they could have been better (Burned Tower, Silph Co, Power Plant, Pokémon Mansion as dungeons, higher Johto trainer levels, higher Kanto wild levels, Lorelei and Agatha somewhere, fixed Johto Gym Leader teams), but they're still my favourite. If they're not your favourite, that's your opinion and that's fine.