You can use Atmel's "Atmel Studio" with an Arduino. To use the debugging features you'll need some sort of hardware debugging tool (such as the Atmel Dragon ($50) or JTAGICE3 ($99)) and you'll probably need to remove the auto-reset capacitor on the Arduino's reset line.
AFAIK, any debugging will require purchasing Atmel hardware of some kind; they've not publicly documented the debug protocols 
Atmel Studio comes with the Atmel Assembler.
There is also the gnu assembler, which is already part of the Arduino distribution. If you add a file with a ".S" extension to your "sketch", it will be assembled rather than compiled. The gnu assembler syntax is somewhat different than the Atmel assembler.
And you can put inline assembler into your sketches. Other ways to Blink ! - #2 by westfw - Frequently-Asked Questions - Arduino Forum has an example.
(The details will be significantly different for the new ARM-based Arduinos like Due.)