I got mine on Black Friday (from Radio Shack for free with a two year contract extension) and it shut down three times the next day. It has shut down intermittently about six more times since. Seems to shut down most frequently right after I turn it on in the morning with either a full charge or 70%+. Using Captivate Keep Alive which hasn't stopped the shut downs. I am waiting for my local Radio Shack to get another phone for me. I got the last one they had and the second from last one went to a friend of the store manager who hasn't had any problems.
I upgraded from an HTC Fuze (WM 6.1) and am otherwise absolutely thrilled with the Captivate. I spent a lot of time researching this phone and Android vs. Windows 7 and am glad I chose it.
Haven't had any GPS problems, can't get Kies to synch my Outlook contacts & calender but need to experiment with it more. Deja Office from the App Store (free) in conjunction with Companion Link installed on my PC synched Outlook but I'd prefer not to pay $40 for the Companion Link.
Overall I love my new Captivate.
update: got a new phone four days ago and no more random shutdowns, the new phone already had the update installed, the first one didn't, GPS seems to work fine too.