Some requirements:
There are only 2 I know:
Flex Builder
IntelliJ Idea
FlashDevelop from FlashDevelop.org is another free editor that appears to be gaining momentum. It's windows-only but seems to be pretty feature rich.
Quite a few prominent Flex+Flash developers swear by FDT
It's an Eclipse plugin, and it's probably the most expensive Flex development tool out there, but it's very good.
Step by step debugging with variable view (and often with additional views like stack or global variables etc) is working in some IDEs. FlexBuilder, FDT3 Enterprise (only the enterprise version allows debugging), FlashDevelop (with extra plug-in). You can also try the (free!) Visual Studio plug-in Tofino (Ensemble), so you can debug inside Visual Studio.
But the best implementation for debugging I found in the Eclipse based IDEs. I'm not much impressed with FDT3 at all, so I recommend FlexBuilder for debugging (+profiling) and of course coding of AS and eventually (visual) design for MXML.
You can try FlashDevelop with the FDB plug-in. Many people prefer this free IDE for coding because of the nice code assist (IMHO the best of all known IDEs). Debugging is working with this plug-in but I wouldn't say that is the "most productive". But give it a try, its free!
I've used them all and I can say without a doubt IntelliJ is the most powerful of them all. http://www.jetbrains.com/idea/features/flex_ide.html
It also is the best JS IDE, and unless you are using .NET on the back end it is probably the best IDE for your back end language. These guys really have it going on.