Wtf? Baron is no problem if you just get enough lifesteal. Anybody can do it pretty much...
I've never had a problem knowing 40 minutes in (as a Bruiser, etc) Hey, i can solo baron now...

I have done it 4 times with fiora.

Jax, Nasus, Udyr, Scion... haven't successfully tried it with anyone else.

End game well farmed Veigar can.

any with life steal lol... ive done it with yi, tryn, fiora, fiddles.

Tryndamere, Wukong, Sion

i did it with caitlyn, ashe, and katarina.. but with katarina that was when gunblade was stackable...

Easily with Sion, and I did it with WW yesterday. Also did it a while back on Cait when I was pretty fed.

As others have said, any fed AD/bruiser ought to be able to solo him. Never tried on any APs, though.

fiddlesticks

Mundo can.