Is there a phrase that means sleeping with someone without sex?

Well with babies we often say 'to sleep(/be) in the bed with'. As in "our baby sleeps in the bed with us."

This extends to adults. Warning... NOTE the use of THE, 'in the bed' is different than 'in bed'!!! Compare 'I was in bed with him' and 'I was in the bed with him'.

Would any of the following examples imply sex....?

• I slept in the bed with him.

• I stayed the whole night in the bed with her.

• They were in the bed together.

It works because 'the bed' is geographical, but 'bed' has many nuances...

You can use "crash with someone".

Example:

I had no place to stay so I crashed with her.

Although not foolproof, it implies less the act of having sex.

Edit: As it's been pointed out, crashing with someone implies some sort of need. You might be too tired to go elsewhere or not have anywhere else to stay.

Edit 2: Some variants I can think of are "crashing at someone's place" or "crashing on someone's couch". If you just use "crash with someone" you avoid telling exactly where you slept.

The phrases below are often used when small children sleep with their parents in the same bed.

To share the bed together (or) share the same bed
To sleep in the same bed

If you lack a spare room, and a guest needs to spend the night, you might offer to share your bed with him or her. This is often the case between close friends and relatives. I have shared the same bed with a cousin, who is more like a sister to me, and with an elderly aunt who felt scared to be alone in a strange house.

I wouldn't say to an acquaintance, "I slept with my cousin last night" that might be misconstrued as meaning we had sexual intercourse. On the other hand, "We shared the same bed" and "My cousin and I slept in the same bed" do not strike me as being sexual in the least.