driving, hard, lashing (esp. BrE), pelting, pounding (esp. AmE)
drenching, heavy, pouring, torrential
steady
drizzling, fine, gentle, light, soft
The fine rain turned to mist in the early evening.
The forecast is for wind and light rain.

warm
cold, freezing, icy
constant, continuous, incessant, persistent
intermittent, patchy (BrE)
overnight
Overnight rain had freshened up the grass.

monsoon, tropical
The monsoon rains started early this year.

spring, summer, etc.
acid

drop
inch, shower, spot (esp. BrE,informal)
We had three inches of rain last night.
A few spots of rain had fallen.
We could do with a spot of rain. (BrE)

forecast
Rain is forecast for tomorrow.

look like, threaten
It looks like rain (= it looks as though it is going to rain).
Black clouds threatened rain.

pour with (esp. BrE)
It poured with rain all afternoon.

get caught in
We got caught in the rain on the way home.

come down, fall, pour down, trickle
beat, drum, lash, pelt, pound (esp. AmE)
Rain beat against the roof all night.
The rain pounded down on her.

drip, patter, splash
She listened to the rain pattering against the window.

drench sb/sth, soak sb/sth
Heavy rain drenched us.

come, set in, start
The rain came just as we set off.
The rain had set in steadily by the time we got home.

cease, let up, stop
The rain didn't let up all day.

continue
The rain continued for most of the day.

threaten
With rain threatening, we headed home as fast as we could.

drive sb
The rain drove the players off the court.

cloud
drop (usually raindrop), water (usually rainwater)
shower, storm (usually rainstorm)
barrel, gutter (both AmE)
gear (esp. AmE)
None of us had proper rain gear.

gauge

in the rain
We found her sitting in the pouring rain.

out of the rain
Come in out of the rain.

through the rain
We drove slowly through the driving rain.

come rain or shine, rain or shine (figurative)
We work outside every day, rain or shine.

hard, heavily
a little, lightly, slightly
non-stop, solidly (esp. BrE), steadily
It had rained solidly for four days.
It's been raining steadily all day.

begin to, start to
be going to
I don't think it's going to rain.

start raining, stop raining

Rain is used with these nouns as the subject:
arrow, bomb, debris