Series 1
Red and Blue
Red first met Blue in Red Meets Blue.
Red, Blue and Yellow
They are the main trio in the series. first seen in "Yellow Meets Red and Blue". Despite that, they are commonly seen with other characters, most notably the RYB secondaries.
Red, Blue, Yellow and Green
These four are one of the the three protagonist groups (RYB + Green or ROYGBP - Orange and Purple). Just them are seen together in "Chameleon", "Silly Colouring", "Green Means Go", and "Choosing Colours".
Red, Blue, Yellow, Green, Orange and Purple
These 6 always do activities and go on adventures together as shown in Little Red Riding Hood, Purple's Patterns, Pick a Partner, Rainbow, Lighter and Darker, A Plate Of Many Colours, The Mixing Factory and Many Mixes Make Brown.
Blue and Yellow
Blue and Yellow are best friends. They first met in Yellow Meets Red and Blue.
Red and Yellow
Red and Yellow first met in Yellow Meets Red and Blue.
Yellow and Green
They do play games together as seen in Lime.
Indigo and Violet
Indigo and Violet are best friends and are colleagues, but they might also be dating.
Black and White
Black and White mix to make Grey.
Black, Dark Grey, Grey, Light Grey and White
They were colouring a city together in grey and afterward even preformed a tap dance in the rain with their umbrellas.
Pink and Brown
in name that colour they competed in a game show hosted by purple
Cyan and Magenta
This is Cyan and Magenta. See here.
Series 2
Deep Blue and Sky Blue
They are explorers. Deep Blue explores the deep sea with his submarine and Sky Blue has a plane. They are possibly old friends since they often call each other Deep and Sky. In Deep Blue and Sky Blue, they met and became friends with Blue who later in Fun with Colours introduced Red, Black, White, and his best friend Yellow.
Mixed
Huey Eight
This group are the eight main hues: the primary and secondary colours in the RYB, CMY, and RGB colour models. The members of this group are Red, Orange Yellow, Green, Cyan, Blue, Purple, and Magenta. They are seen forming a colour wheel in "Colour Wheels".
The Printing Crew
This group rides on ink cart-tridges in the Printing Zone and create printed pictures. They are based on the CMY(K) colour model. The members of this group are Cyan, Magenta, Yellow, and Black, the latter of which joined them in the episode Return of the Printing Crew. They are also best friends.