To find out what the current IP address assigned to your iPhone is turns out to be pretty simple if you know where to look.
First, select Settings from your SpringBoard. Next, select Wi-Fi from the resulting Settings menu. This results in a list of available networks being displayed under the Choose a Network… label. To the right of each listed network is a right-arrow icon. Find the network you are currently connected to in the list (it has a tick next to it) and click on the right-arrow icon.
This will bring up the detailed network information, listing among other things the IP address your iPhone is currently assigned with from that network’s DHCP server.
Nifty.