Resize your sig a bit, beautiful, it's too large.
To answer the question... Is somewhat difficult. I guess the actual gameplay itself + physics + the other aspects linked in to all of that are the aspects I can appreciate/admire the most. I found the actual platforming element much more fun and rewarding than other platforming games I've played, and I enjoyed the weapon system. The idea of "leveling" a weapon up/risking downleveling if hit is a fairly unique reward/incentive system. Oh yeah, and I enjoyed almost all of the boss fights, so I don't mind doing a boss rush every now and then.
On a more personal/subjective level, the characters and story. I'm really itching for a prequel and/or sequel to introduce some new characters as well as expanding on the ones we've already seen. I'm really not too keen on the possible sequel having an entirely new cast and I hope that's not the direction it'll take, even though I'd play the hell out of it anyway.
But that's just me. I've traditionally been into heavily story-based games with complex character-driven plots, so when I see potential for development in that field, it's like an itch I can't quite scratch. I do think Cave Story, by it's nature, runs the risk of possibly being too bogged down with story/dialog, but it could have reached a bit further and there was potential to convey a narrative in ways other than just dialog. *
Ranty.
* Edit: To stipulate, I spent a lot of my time in Cave Story trying to interact with objects to see if they'd tell me anything. Basically, provide some narrative and contribute to my understanding/appreciation of the setting. For example, in Baten Kaitos, exploring the scenery on different continents will show you the differences in culture between one nation and another down to some quite fine details. In Golden Sun, I remember you being able to peer into villager's ovens and receiving commentary on the regional cuisine of each area. That sort of... flavor text, I guess, adds a whole new layer to a game for me.