Can I use Wi-Fi only on my iPhone with no sim card?

I got this iPhone 4 from someone because they switched services and phones and I'm waiting for my straight talk sim card to come in so my question is can I use Wi-Fi without being charged?

Yes definitely. Wi-Fi is free and no need for a sim card.

Yes, you can definitely use Wi-Fi on your mobilewithout a sim card. A Wi-Fi device only needs a wireless router with internet connection.

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.