Fighting a dragon, at least in the videos, looks to be combat focused (as it should be) so armor, weapon skill, and magic skill all aid in killing a dragon. My question is, would a thief-type character (or a non-destruction mage) still be able to kill a dragon?
Earlier on you'll have to be a total wimp and kite the dragon around, plinking at it from cover with your bow. Be sure to keep lots of ammo.
Later on, I'm currently level 25 and I've assassinated a couple of slumbering dragons with one well placed backstab(with a dagger, of course). Just make sure your Sneak and 1-hander skill is solid if you wanna try that though.
If you are a dagger type thief, just let the dragon fly away, then move to his direction. Usually he will be standing on a dragon wall, so just sneak behind him and attack him... This can grant you a one hit kill sometimes if you have the Assassin's Blade perk, a good dagger and the Dark Brotherhood gloves...
Conjure a flame atronarch and let her fireball it while you safely barrage the dragon with poisoned arrows and use potion to boost your archery damage. Invisible spell is truly handy if you're alone. Be patient. Keep attacking, stay alive and you'll eventually own it. I'm an assassin/thief, using sneak style archery and one handed for quick and powerful battling. I'm a Khajit.
You can get one hit kills as an assassin if you leave your left hand empty and have a good dagger in the right hand, as well as the shadow warrior perk. (need the assassins blade perk too, duh!)
Walk up to the landed dragon, when you are close, go to stealth and immediately stab. You will at least get the 15x or 30x (if you have the shrouded gloves) and often go into a mini-sequence of brutally stabbing it in the head. If you just get the 15x damage, unstealth, restealth and stab immediately again. usually by the 3rd shot you will be on the dragons back stabbing it in the brain.
Oh, and if you do this at the right time when a bear is attacking you, I have seen an animation where you thrust your arm down its throat and the twist your arm for an instant kill.
Funny to do on slaughterfish hehe, all this crazy animation and what not for just killing a fish :)