At least, not as easily as having them classified for you by UnitAura().
But if you're just looking for this information on-screen (as opposed to building it into your own addon or something),this is the sort of thing Auracle (http://www.wowace.com/addons/auracle/) was designed for.
You'd have to manually assemble a list of debuffs for each category (i.e. stun = Kidney Shot, Cheap Shot, Hammer of Justice, Bash, ...) but it would then let you easily see which categories of debuff were active.
Thanks, guys. looks like I wasn't 100% clear but you have worked-out what I really meant! I know UnitAura doesn't give this information, was looking for debuff type via something else. Great info I'll check-out your suggestions.