Yes, they do do it. It is called a 'natural' cycle, or else you can take something like clomid (if you don't O regularly) and then it is called a 'minimal stimulation' cycle, or something like that.

My understanding is that some clinics don't like to do it that much because it can be more expensive and less successful - because they only have one egg to work from each cycle, rather than 10 or more that they often get when you have the drugs. If you are going to a clinic, ask them about it - the clinic I go to has an info booklet on it. It is good to read about it and discuss it with your FS to decide which option would be best for you and your DH.