Let's see...
Keep in mind I'm taking a wider rage for black/brown, erring in the side of caution for this. Many of these might be contentious.
Street Fighter:
- Balrog/Boxer, who's represented by Little Mac.
- Dee Jay, represented by Diddy Kong
- Dhalsim, not an encounter
Zelda: (most of these are particularly contentious, given the whole fictional ethnicity thing. The Gerudo are certainly meant to be brown/black coded, the rest... probably not.)
- Impa (do Sheikah count? they tend to have darker skin that Hylians...), represented by Sheik
- Koume & Kotake (Gerudo), not an encounter
- Twinrova (Gerudo), not an encounter
- Ganondorf from Twilight Princess (Gerudo), represented by Ganondorf
- Urbosa (Gerudo), represented by Zero Suit Samus
- Tetra (Hylian, kinda pushing it, relatively dark skinned, most likely tanned), represented by Toon Link
- King of Hyrule (Hylian, dark skinned, not likely tanned, given he's a boat), not an encounter
- Din (Hylian??? Goddess?? relatively dark skinned???), represented by Zelda
- Ganondorf character spirit, not an encounter
F-Zero:
- Baba (he's... an issue), represented by Captain Falcon
Punch-Out!!:
- Mr. Sandman, represented by Donkey Kong
- Great Tiger, represented by Incineroar
- Super Macho Man, not an encounter
- King Hippo (Vaguely Pacific Islander?), represented by K.Rool
- Bald Bull (Turkish, dark skin?), represented by Little Mac
- Doc Luis, represented by Little Mac
Splatoon:
- Off the Hook (one of them is Marina), represented by Inkling
- Octoling Girl and Octoling Boy (debatable, renders used are the lightest skinned versions they had :| ), represented by Inkling
Xenoblade:
- Elma, represented by Bayonetta
Bayonetta:
- Rodin, not an encounter
- Loki, represented by Sheik
Ever Oasis:
- Tethu, represented by Young Link
Shantae:
- Shantae, represented by Zero Suit Samus
ARMS:
- Twintelle, represented by Bayonetta
Those are all the Black/Brown spirits in the game. If I missed one, feel free to point them out.
Also if you're thinking, "hey, doesn't this series have black characters", yeah, probably, they're just not spirits.