deep
light
much-needed
I'm off to bed for some much-needed sleep.

adequate
REM

drift into, drift off to, drop off to, fall back to (AmE), get to, go to
She turned over and went back to sleep.

cry yourself to
There are nights when I cry myself to sleep.

catch, get, snatch
Close your eyes and get some sleep now.
I snatched a few hours' sleep in the afternoon.

need
survive on
They seem to survive on only a few hours' sleep a night.

induce, promote
the use of drugs to induce sleep

lull sb to, send sb to
The quiet music soon sent her to sleep.

drift in and out of
He drifted in and out of sleep all night.

lose (often figurative)
Don't lose sleep over it—we'll sort everything out in the morning.

disrupt, disturb, interrupt
catch up on
I used Saturday to catch up on my sleep.

feign
I feigned sleep when the nurse came around.

come
Sleep came to her in snatches.

overcome sb, overtake sb
Sleep finally overtook me.

cycle, pattern, schedule (esp. AmE)
deprivation, loss
disorder
apnoea/apnea
aid (esp. AmE)
the nation's most commonly prescribed sleep aid

during sleep
a decreased heart rate during sleep

in your sleep
He often walks and talks in his sleep.

a lack of sleep
I was suffering from a lack of sleep.

a wink of sleep
I won't get a wink of sleep with that noise downstairs.

long
little, short
dead, deep, heavy, sound
uninterrupted
good, restful
light
disturbed, exhausted, fitful, restless, troubled, uneasy
I woke up early after a disturbed sleep.

dreamless, peaceful
drunken
beauty
Sorry, but I need my beauty sleep.

need
have
Did you have a good sleep?

be in
I was in a deep sleep when the phone rang.

drift into, fall into, sink into
I immediately fell into a dead sleep.

awake (sb) from, awaken (sb) from, wake (sb) from
He woke from a fitful sleep with a headache.

a good, poor, etc. night's sleep
You'll feel better after a good night's sleep.