OK, for a 6 gallon tank, appropriate fish:
Betta splendens: 1 male or 1 female (room for more fish) - also other similarly sized betta species.
Dwarf Puffer: 1 male or female and one more female - no other fish
Mystery Snail: 1 with room for fish, 2 without
Amano Shrimp: Up to 12
Neocardinia spp (Red Cherry, Crystal Red, Blue Buddha, Bumblebee Shrimp): up to 4 per gallon.
African Dwarf Frog: up to 2
Japanese Ricefish: Cool water - up to 4
Javanese Ricefish: Up to 5
Dwarf Medaka: up to 10 (tolerant of water up to 35ºC)
Many species of Killifish: Species Tank. Requires further research. Need to be replaced annually.
Sparkling Gourami: 2 or 3 (one male)
Otto: up to 8 in a well planted tank with supplamental feeding. No more than 1 without. (I have one in a 5.5)
Aspidoras spilotus, A. raimundi: Cory like fish - 5 - no more, no less.
Corydoras gracilis, C. Guapore, C. osteocareus, C. Panda, C. similis: No fewer than four, no more than 6
C. pygmeus, C. hasbrosus, C. hastatus: Up to 12, no fewer than 6 - feed live or frozen daphnia at least occasionally.
Many many species of small tetras, in schools of 6 to 12, including especially: Neons, Glow Light, Black Neons, Green Neons, Cardinals, Embers, Flame (Von Rio), Kerri, Dawn, Gold
Smaller Apistogramma species: Mated pair only, well planted tank, lots of hiding spaces, and you'll have to cull all the fry.
Microrasboras including:
Boraras brigittae (red finned
Dwarf Rasbora), B. maculatus (Spotted
Dwarf Rasbora), B. merah, B. micros, B. urophthalmoides (Exclamation Point Rasbora) - up to 15, Also Galaxy Rasbora
Small Rasboras:
Trigonostigma heteromorpha (Harlequin), hengeli, and espi - 6 to 10
White cloud mountain fish - Maybe as many as 12
Been meaning to do this for a while now. More later....
Note, this is not dogma. This is a best guess on my part based on the limited information I have for these fish. I, for instance, would not keep Harlequins in a 6 gallon tank. I have a dozen in a 75g and they use all of it. So while the numbers work out to 6 to 10, I think they would feel cramped. Willing to hear arguments for or against any positions. (Except on bettas. That argument is tedious and I don't intend to hear it.)