Cool Blues
Cool blues are those with a green bias. There are many of them - Phthalo Blue, Prussian Blue, Cerulean blue, Manganese Blue, Winsor Blue and so on. It is useful to have one cool blue and one warm blue in a split primary palette. Phthalo Blue is perhaps the most common, but some prefer Prussian Blue as it is less permanent and easier to control. Cerulean is useful as an opaque blue and is a common addition in watercolour palettes especially for painting the sky. I like to have Cerulean Chromium and Phthalo Blue to have a transparent and an opaque option. To see a paint-out with comments on a huge range of blues in many brands see my Blog post here. To see all the blue watercolours I have tried see here.
Phthalo Blue

Phthalo Blue (Green Shade) PB15.3. Daniel Smith.
Phthalo Blue is also known as Winsor Blue, Monestrial Blue and other names. Its pigment name is, as always, most helpful. It is an highly transparent, high staining and non-granulating blue as the particle size is extremely small. It is rated ASTM II for lightfastness so is reliable as a watercolour. It neutralises with an orange-red.
PB15 made from copper phthaocyanine.
PB15 made from copper phthaocyanine.
Pure Bright greens - Phthalo Blue + Hansa Yellow Light

Phthalo Blue(left) mixed with Hansa Yellow Light PY3 (right). Daniel Smith paints.
When a cool blue such as Phthalo Blue is mixed with a cool yellow such as Hansa Yellow Light, the greens that are produced a very bright and vibrant since there is no red in either paint to neutralise or dirty the mixture. Other cool blues that will produce simimarly pure greens are Prussian Blue and Cerulean, though the greens made with cerulean are more opaque.
Mid Greens - Phthalo Blue + Quinacridone Gold

Phthalo Blue (PB15.3) with Quinacridoe gold, Quinacridone Deep Gold (PO48) and Quinacridone Sienna. Daniel smith paints.
Phthalo Blue mixed with Quinacridone Gold gives a range of lovely mid greens.
Amazing mixes - Phthalo Blue + Quinacridone Burnt Orange

Phthalo Blue PB15.3 (left) mixed with Quinacridone burnt Orange PO48 (right). Daniel Smith paints.
With more of an orange, the range of colours possible with Phthalo Blue is quite remarkable. Some artists use Quinacridone Burnt Orange instead of Burnt Sienna.
Phthalo Blue with common palette colours.

Phthalo blue mixed with cadmium Yellow Light, Cadmium Yellow Deep, Quinacridone Sienna, Cadmium Red Medium, Permanent Alizarin, Quinacridone Rose, Quinacridone Violet, Imperial Purple, Ultramarine, Indigo, Manganese Blue, Buff Titanium, Phthalo Green, Sap Green, Raw Sienna, Burnt Sienna, Indian Red and Burnt Umber.
Bright yellows - Cerulean + Cadmium Yellow Light

Cerulean PB36 (left) mixed with cadmium Yellow Light (right).
Cerulean Blue is an opaque blue, so can make useful mixes if a covering bright green is needed.
Phthalo Blue (Red Shade)

Phthalo Blue (RS). Daniel Smith watercolours.
Also made from PB15, but a warmer version, closer to a mid blue. This is a less useful version for mixing but I love it as a colour. It neutralises with a red-orange.
Cerulean Blue (Chromium)

Cerulean Blue Chromium. Daniel Smith Watercolour.
Made from PB36.
There are a number of other blue and turquoise blues made from PB36. I like this one, mixed with Ultramarine, for blue skies anywhere in the world. It is granulating and liftable, which is very important when doing skies so you can lift out the clouds.
There are a number of other blue and turquoise blues made from PB36. I like this one, mixed with Ultramarine, for blue skies anywhere in the world. It is granulating and liftable, which is very important when doing skies so you can lift out the clouds.