Although with the current level cap at 50. I really only find it feasable to solo Wolves caves for like a level 40+. And thats ASSUMING your even an offensive class.
Sure, you "could" solo wolves caves with a level 45 FS Priest....but it'll be slow as *******. But at that level, there isn't a shortage of people legitly running those dungeons that wouldn't mind having an over-leveled character joining them. Even if it's a support class or weird class like FS Sorc.
I solo'ed Leviathan with a tank at Level 36, so that is not really as hard. We solo'ed the Payon ruins with a Little over 40.
What seems impossible even with L50 was soloing the abandoned lab, since the last Boss summons this crazy super moth when you are too slow killing his circle of enchanters.
However, we are looking Forward right now to see the first one soloing the hell of deadly poison, although that is really, really tough.
I would argue there is no way soloing any dungeons after Alberta. The ghost ship is just too damn tough and lets not even talk about the fortress.