In light of newer regions and games, Kanto has its notable problems. As others have mentioned, the lore and plot around the region are both pretty lacking. You as a player just know that you want to see the region, catch and train Pokémon, and knock down the baddies. It works as an introduction to the series; however, when looking at the other regions that do themselves a service with attention to lore and plot, Kanto looks bare bones.
@Aki put it well, but the layout of the region is just neat and, geographical features aside, one of the most interesting to traverse. Sneaking below towns to other ones and actually visiting the skipped towns later feels different and right. I don't know how many people cared for the point of no return at Cerulean City, but I always appreciated that. It made me feel like the stakes had ramped up and that I was heading toward bigger and better places. It also made the return trip to Pallet Town through Diglet Cave all the more satisfying. Touching on base with the
Gating Content thread, Kanto had enough variance with roadblocks that made conquering them all a giddy time. You got to get past the impossible Cerulean ledge, Snorlaxes, bicycle passes, and more, and combined with the twisty map design, it makes you feel like you're really unlocking the region as you go through it.
My favorite memories include exploring the Seafoam Islands and Unkown Cave for the first time as a kid, and in my recent playthrough on the e-Shop copies, I surprisingly had a blast with hunting down the Safari Zone Pokémon and striving for Pokédex completion (which never quite happened since my roommates/classmates stopped playing, :worried:). And of course, I enjoyed every sneaky moment when your rival challenges you out of the blue.