Can I run Samsung apps (app market from Samsung) without a SIM and mobile connection? I have a Samsung Galaxy S with Android 2.2.

I have read that now there is a "Kies" app available from Samsung which would allow to upgrade the OS on the phone without connecting it with the USB cable to another computer.

That article said I have to install it through the "Samsung apps" app. So I started it, but it said it won't work without a SIM card.

But I intended to use only WiFi, I don't need the SIM card and the mobile connection.

Why this problem? Is it solvable (without a SIM card)?
No, the Samsung apps market won't start without a SIM card, because the card is used to determine the country of the user.

There is an App called "Kies Air" which allows you to connect your device to the Kies App installed on your PC over WiFi. But I doubt that you are able to upgrade the OS this way. It's more meant for synchronization (calendar, email, ...) use.

IMHO you need a USB cable to update the SGS, either with Kies or Odin/Heimdall.