-- The Boros Legion (red/white)
-- The Golgari Swarm (green/black)
-- The Selesnya Conclave (green/white)
-- House Dimir (blue/black)
-- The Orzhov Syndicate (white/black)
-- The Izzet League (blue/red)
-- The Gruul Clans (red/green)
-- Azorius Senate (white/blue)
-- The Cult of Rakdos (black/red)
-- The Simic Combine (green/blue)
The shards from Shard of Alara are (with guilds to build them in brackets):
--Bant is White Green Blue [Selesnya, Simic, Azorious]
--Esper is Blue White Black [Dimir, Orzhov, Azorious]
--Grixis is Black Blue Red [Rakdos, Dimir, Izzet]
--Jund is Red Black Green [Rakdos, Golgari, Gruul]
--Naya is Green Red White [Gruul, Boros, Selesnya]
There are also three color combinations that are not shards. When these are combined with the shards, we get an even repetition for all Ravnica guilds of three times. These have names from an early set that did not receive wide use.
--Ana is Green Blue Black [Simic, Dimir, Golgari]
--Ceta is Red Green Blue [Gruul, Simic, Izzet]
--Dega is White Black Red [Orzhov, Rakdos, Boros]
--Necra is Black White Green [Orzhov, Selesnya, Golgari]
--Raka is Red White Blue [Boros, Azorious, Izzet]
Khans of Tarkir redefined the wedges:
--Abzan is White/Black/Green
--Jeskai is White/Blue/Red
--Sultai is Blue/Black/Green (some refer to it as BUG)
--Mardu is White/Black/Red
--Temur is Blue/Red/Green (some refer to it as RUG)
That's 20 decks to cover all of the combinations. Adding 5 monocolored decks and the possibility of an artifacts-only deck, that puts us at 26 decks. With the addition of colorless as a third color, we also have a new range of three-color combinations (ten of them).