NO! - Well at least not regularly. Although there are times when a child may need added security for a night (thunderstorm, nightmare) ideally children should have their own room.
Newborns should NEVER sleep with you! This is simply because there are all to many tragic cases of newborns being accidently smothered by blankets, pillows, or the parents themselves.
Newborns should sleep in their own crib from the first day they come home. (Click here for my best picks!) Keeping the crib in your own bedroom with you is great, but kids should have their own room by the age of 3. This is because there are essential developmental benefits from having your own dedicated personel space.
Independance
My parents see me as my own complete person all by myself.
Identity
I can express my own unique personality through interior design.
Confidence
I can do things all by myself.
Coping skills
I can process thoughts and emotions and independanly.
Creativity
I get to use my imagination decorating.
Focus
I can study and play without distractions.
Responsibility
I have to maintain a clean and organized space.
Structure
My room was given to me by an athority.
Security
This is the one place in the world where I'm most safe.
"But won't my child feel unloved or rejected if I deny their request to sleep with me?"
No - Not if you are providing an abundance of love in all other areas.
"Can they deny me entry?"
Yes and no. See: "Privacy"
Summary
Ideally, children should have their own room. However this is not always practical. Although some kids like sharing a room, most will prefer their own room at some point.