Is it possible to use an iPhone without a SIM card as an iPod touch?
There is an Apple support document on how to do this.  You don't need to keep a sim in the phone but you need to put one into it to activate it before taking it back out.

Here's the procedure for 3G and 3GS:  


  You can use any SIM card associated
  with the carrier that your device
  supports to activate the phone. Simply
  place a SIM card from the last carrier
  with which you used your iPhone into
  the device, and activate it. Then
  remove the SIM card. You can now use
  the iPhone 3G or iPhone 3GS as you
  would an iPod touch (Wi-Fi only, no
  cellular service).
  
  Note: You can use the activated SIM card from your new iPhone to do
  this.
  
  To re-activate an iPhone 3G or iPhone
  3GS that displays the "Connect to
  iTunes" screen:
  
  
  Insert a SIM card from the carrier with which you used your phone. Note:
  If you are using the same carrier, you
  can use the activated SIM card from
  your new device to do this. If your
  device is unlocked by your carrier,
  you can use any SIM card.
  Connect the iPhone 3G or iPhone 3GS to iTunes on a computer connected
  to the Internet. iTunes will then
  activate the device. You can remove
  the SIM card at this point and use the
  iPhone as if it were an iPod touch.