Dex is considered "facilitated arousal" so I think that when the patient is in the sleeping mode, they don't remember this, but when they are aroused, they do remember - just like anyone who is sleeping.
There is very GOOD evidence that clonidine prevents perioperative MI's. In fact, I think the numbers are as good as beta-blockers.
I read an article last year (can't find it but I know it exists) that compared precedex to propofol for pedi MRI's and as expected, precedex had a much lower incidence of airway problems and morbidity. However, as expected, time to dischare was much greater.
I have used it for many things as mentioned above (airway cases that need spontaneously breathing patients, awake fibers, adjunct to general anesthesia, MAC cases) and would love to try it for other things (awake crani for one.) I think it is a wonderfully useful drug as JPP said.
I want to mention one place I used it that made my life SOOOO much easier. We treat a lot of shot up marines that recently returned from IRAQ and if you have had the great opportunity to do this, you know what a joy it is. They are CRAZY cuz i guess they come out of anesthesia thinking they are in a prison camp or something because they wake up swinging, etc. I even had one try to BITE me! Anyway, we were doing a case on a guy that had severe chronic pain issues and a very large opioid requirement and he had a history of waking up very, very poorly despite the multiple attempts at a smooth wakeup - plus, if any body deserved a ketamine infusion, this guy did, but I knew that would also potentially make his wake up and PTSD wake up worse. So, I ran precedex and ketamine (.25mg/kg/hr) through the case and turned off the ketamine ~45 minutes before the end of the long case and kept the precedex going. I extubated him with the precedex on (he was spontaneously breathing and opening eyes so it was an "awake" extubation) and then took him to the pacu. He chilled in the PACU for 1.5 hrs with no problems. It was very smooth.