Why does the sea look blue when water is colourless?

Two effects combine, and one of them surprises people: water is not actually colourless.

Water genuinely absorbs red light. Water molecules absorb light at the red end of the visible spectrum through vibrational transitions, far more strongly than at the blue end. In a glass the path length is too short to notice, but over metres the effect becomes visible: red is removed first, then orange and yellow, leaving blue. This is why underwater photographs without artificial light are overwhelmingly blue-green, and why a deep swimming pool of clean water looks blue even with white tiles.

This is a genuine absorption effect, and it is the dominant reason deep clear water is blue.

Reflection of the sky contributes too, particularly at shallow angles and on calm surfaces, which is why the sea looks greyer under cloud and bluer under a clear sky. But it is a secondary effect, not the main explanation — which is the correction to the common answer.

Why the sea is often not blue:

Green seas usually indicate phytoplankton, whose chlorophyll absorbs blue and red and reflects green. Productive coastal waters are green for this reason, and satellites measure ocean colour to estimate plankton abundance.

Brown and murky water contains suspended sediment, stirred up by rivers, tides and storms.

Very dark or tea-coloured water, as in peat-fed lochs and the Rio Negro, contains dissolved organic matter from decaying vegetation.

Turquoise shallows over white sand result from light reaching the bottom and reflecting back through only a short path of water.

How this differs from why the sky is blue. The sky is blue through Rayleigh scattering — shorter wavelengths scattered more by air molecules. The sea is blue mainly through absorption of red. Two different mechanisms producing a similar colour.