does gps work without sim card?

yes. won't work without it.

The GPS does work without a SIM card installed. GPS apps from the app store that display location as latitude/longitude/altitude will work without the SIM (although it will take longer to do the localization, and it will only work out in the open, since without the SIm the GPS must function without the assistance of the cell towers.

However, Maps will not work without the SIM, unless you're on Wi-Fi, since the map data that your location is shown on must be downloaded from the internet.

ok, so without wifi all you will see is a blinking blue dot on a gray screen?

Correct.

Maps data is downloaded from Google via the internet with a wi-fi or cellular data connection.

whats the use? A blinking blue dot on a grey screen. In my opinion it doesn't work if that's all you get.

What is the use of a GSM phone without a SIM card?

The iPhone includes A-GPS, short for assisted GPS. It is assisted by cell tower location and wi-fi networks to speed up the location services with GPS, and it is assisted with maps data that must be downloaded to the iPhone via the internet - just as when accessing Google Maps on your computer. Hand held stand alone GPS devices have maps data for a given location installed/available direct on the device without internet access required. That is not A-GPS.

A blinking blue dot on a grey screen. In my opinion it doesn't work if that's all you get.

As mentioned in the above thread, there are app store apps (TrackThing, gpsCompass) that will read out your actual position, speed, direction, in numbers, so you can see where you are on a map. (You remember maps? those quaint old world methods of finding where you are?).

This is quite useful in the back country, where cell signals may not reach. I've used gps Compass in the mountains where there was no cell signal. In my case it took about 2 minutes to find the satellites the first time but after that it was very fast.

Its not a substitute for a Garmin, but with a paper map you can still find exactly where you are, and were you are going.
(If you don't know how to navigate with maps, compass, and longitude/latitude numbers, you probably don't belong where there are no cell signals.)