Heres a list of classes that can complete dungeons in a reasonable manner. For the builds see
viewtopic.php?f=32&t=270 and
viewtopic.php?f=32&t=269, although some of the alltime records arent possible anymore (mostly the ones with necrotic traversal in the bar).
Catacombs of Kathandrax
any class x/A with sf and enough single target dmg to kill various bosses
Rragar's Menagerie
shadowform dervish with grenths aura (hard part: getting the key on tier 3)
Cathedral of Flames
shadowform dervish
Ooze Pit
A/D or D/A with shadowform and grenths aura, pretty easy to do
Darkrime Delves
A/N or A/Me with parasite or empathy are the easiest
Frostmaw's Burrows
whirling ranger (learn your snowballs)
Sepulchre of Dragrimmar
A/E with sliver or R/A with whirling, pretty easy to do if you re not going for a fast time
Ravens Point
shadowform dervish with grenths aura (lots of RNG on last tier)
Vloxen Excavations
shadowform dervish with grenths aura (super hard dungeon to do solo)
Bogroot Growths
VoS dervish, pretty easy to do if you re not going for a fast time
Bloodstone Caves
shadowform dervish with grenths aura
Shards of Orr
shadowform dervish with grenths aura (have to pull properly)
Oola's Lab
x/A with shadowform and stone for bosses, pretty easy to do
Arachni's Haunt
whirling ranger with mental block and antidote signet, lots of RNG
Slaver's Excile
A/E with sliver, also possible as R/A with whirling (bring swap for each), pretty easy to do if you re not going for a fast time
Fronis Irontoe's Lair
any class, super easy to do
Secret Lair of the Snowman
Me/E or E/Me with obsidian flesh and wastrels, also possible as R/A with whirling, pretty easy to do if you re not going for a fast time
Heart of the Shiverpeaks
shadowform dervish with grenths aura, pretty easy to do if you re not going for a fast time