DO NOT REMOVE THE SIM!
To continue using your original iPhone without active cellular service, leave the inactive SIM card in place. You will be able to use the iPhone as you would an iPod touch (Wi-Fi only, no cellular service) as long as you keep the SIM with which it was last used, even if you update or restore the operating system of the original iPhone.
Activation for an original iPhone requires that its SIM card stays with that iPhone. If the original iPhone displays the "Connect to iTunes" screen, you can use that SIM card to re-activate the iPhone, regardless of whether that SIM has a wireless service account/tariff still associated with it.
To re-activate an original iPhone that displays the "Connect to iTunes" screen:
Reinsert the SIM card used when the original iPhone was activated and had a valid wireless service account/tariff.
Connect the original iPhone to iTunes on a computer connected to the Internet.
If that SIM was previously valid and used with that original iPhone, iTunes will re-activate the iPhone, but without any cellular service.
Additional Information
If you no longer have the SIM that was used with the original iPhone, and the original iPhone displays the "Connect To iTunes" screen, contact your carrier to get a replacement SIM.
If you don't already have a wireless service account/tariff with that carrier, iTunes will help you create one.
The statement above is directly from Apple. You CAN remove the SIM if you have a 3G or 3GS but not the "2G" original iphone.