Short answer is you can’t.
At least I have not been able to find a procedure or free app that does this. I found some web pages that say to use the Call button to dial the last call in the recent list. The use of the Call button on the keypad gui didn’t work for me. Still requires multiple key presses and did not bring up the last dialed number as stated.
Update: the Call button method will use the last dialed number, not the most recent number in the Recent list. So, using Call is a viable approach.
So what to do? The easiest way I found is to add the target number to your favorites list. Now to rapidly redial just tap the contact in the Favorites list, then tap the Speaker icon. Busy? Just tap “End call”. Repeat.
My question: why doesn’t the iPhone have a real redial capability, other smart phones do? Is it some kind of industry requirement or for reduction in negative possibilities?
May 28, 2014: As I noted here, Samsung Galaxy S5 does support auto redial.
August 12, 2011: Anything changed about this feature or lack thereof? I am still using the first iPhone (yup, doesn’t even update anymore, and the fake GPS map doesn’t even work). Do the newer iPhone or Android phones have this feature built in?