Can I use my iPhone4 without a sim card if i just updated to the lastest software? I have an iPhone 4 that I wanted to use for my daughter to play on. I updated it to the latest software iOS 6 and it's telling me to put a SIM card in to activate it. I don't want the iPhone activated. I have wifi in my house and I just want her to be able to play games on it. Is it possible?
No - if the device is waiting at the activate screen it won't run normally. Yes - once the activation is done, you can pull the SIM card. 

Activate means that the OS becomes usable. Unless (and until) your phone gets jail broken or authorized unlocked (contact your carrier), by design you need a carrier SIM to activate the phone after each restore. 

Major OS upgrades usually include a restore / activation step so you can check here before the next upgrade if you wish to avoid this in the future. 

I've had good luck using an old SIM card that no longer is on an account to keep a proper SIM in the phone. Again, your carrier can help if reusing any old SIM you have doesn't work.