[nudephil (OP)]

Nicky sent in this question:

If the atmosphere were 100% pristine and clean (in theory, of course) would we still have rain? I know that droplets form around solid particles in the air...

What do you think?

[alancalverd]

Yes, but probably less frequent, heavier downpours, with more hail and snow.

[Petrochemicals]

Is the op thinking of cloud seeding,

https://en.m.wikipedia.org/wiki/Cloud_seeding

As alan states cloud seeding draws rain from airborne water with more regularity, when conditions are not optimal  for natural precipitation.

Edit:

Alan states heavier downpours

[evan_au]

Even without dust, some bacteria appear specialised to act as nuclei for clouds and snowflakes.

It is thought that these bacteria are dispersed in winds, and fall to Earth as raindrops and snowflakes. Many of them attack plants through frost damage.

See: https://en.wikipedia.org/wiki/Bioprecipitation

In teh absence of human-produced pollution, natural dust, volcanic ash and salt spray can act as water nucei.

See: https://en.wikipedia.org/wiki/Ice_nucleus

[OliVDB]

Yes, the clouds would more or less keep existing until overloaded, resulting in a really heavy and powerful rainstorm every once in a while.
But I don't think it'd be possible to have the cleanest, purest air, because even if there were no humans, or even no animals at all to kick up dust with their activities, you'd still have wind picking up sand from deserts, volcanic activity and other sources of solid particles in the atmosphere.