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"Overworld/Submap Collection" is the overworld theme ("Terra") from Final Fantasy VI. But that one's pretty easy.
"Volcano Castle" sounds like a lo-fi version of "The Holy Intruder" from Secret of Mana. https://www.youtube.com/watch?v=9CS0dk0jcJY
Looks like this .txt file lists a couple more from Mega Man X and Mega Man & Bass: http://www.romhacking.net/hacks/snes/patches/1467readme.txt
Haven't got the foggiest idea about the rest.
Edited by KDNot sure about the specific songs linked, and haven't heard most of these (though a few sound oddly familiar...) but found some in the comments:
Sunset Beach is Search Man's theme from Mega Man 8
Calm Grasslands is from Chrono Cross according to the comments (don't know the specific song though)
Digital Forest is Astro Man's theme from Mega Man 8
Grinder Base is Crazy Gadget from Sonic Adventure 2 Battle
Beach Level (Unnamed)... I swear I've heard it and am 99% sure it's from a Kirby game (sounds very Kirby-esque at least) but can't remember WHAT game... also I'm getting slight Parodius vibes from Vanilla Dimension but listening to the soundtrack again I'm not sure that's it
Edited by Zanreo My favorite failed console tbh

From this playlist of a prototype of Super Mario World: The After Years:
https://www.youtube.com/watch?v=ZTA27ggllYI&list=PLD08277055519E4AF
https://www.youtube.com/watch?v=Hn4BTbNU_qo&list=PLD08277055519E4AF&index=8
(There are videos I still have yet to watch, and if anyone could just list everything from the playlist for me, I'd appreciate that even more.)