Is there a class of chemicals that change colour depending on whether
they are wet or dry? Could they be incoprated into a paint, glaze or
plastic?

I've used pale pink emulsion paints that dry brilliant white (e.g.
"Indicoat" in the UK), but this process doesn't seem to be reversible.

The short answer is NO. There are compounds that change color with
varying humidity, but they require exposure to the atmosphere. If one
were to incorporate these compounds into a paint, glaze, or plastic,
they would be sealed off from the atmosphere. (I have 45 years
experience in the paint industry...I know whereof I speak.) Even apart
from that insurmountable problem,
no paint manufacturer would touch such a project.
  So, what's wrong with a hygrometer suitably placed? They are much
more accurate than color-changing chemicals.
monroe22

Self-indicating silica gel is the only thing I know which changes
color depending on whether is wet (pink) or dry (blue). It's just
regular silica gel with a cobalt chloride indicator added, which is a
very toxic stuff by the way.
There are other less dangerous silicas (check here  
http://www.geejaychemicals.co.uk/cobaltchloride.htm  )
I've worked with these substances for years and the process can be
reversed anytime and as often as you want, but I really don't think
they can be used as additives in a paint.

There is a liquid spray that is used for checking welds.  They spray
this stuff on the weld, and if the weld is leaking (I'm talking about
extremely micro-leaking... VERY VERY small leakage), this stuff will
turn pink.  Basically, if you have a hairline fracture in the weld,
and water is hardly leaking through at all, this stuff will let you
know.  It might be some form of the silica gel... I'm not sure.  You
can probably search for 'weld crack detection' or 'weld leak
detection'... something like that.  It might be kind of expensive,
since it's highly used in the nuclear power world...  anything that
has a 'nuclear' stamp is typically 5-10 times the price...

What about those pencils that change color when wetted with saliva?

I know of two products that have this property.  An Elmer's glue stick
which goes on pink and dries clear and there is a wall spackle that is
pink when wet and white when dry.