I have done it with both Vlad and Nunu. Just had enouph Ap to keep myself healed.

You can pretty much solo baron with any champ, especially if you use 3 wards.

http://www.youtube.com/watch?v=VWHJXU1_JMc

http://www.youtube.com/watch?v=5zJ43...eature=related

http://www.youtube.com/watch?v=fNbc4...eature=related

http://www.youtube.com/watch?v=3FbuN...eature=related

http://www.youtube.com/watch?v=t-IOX...eature=related

http://www.youtube.com/watch?v=dn9ee...eature=related

hope those links answers your question


PS: this are not my videos i seen it on youtube

almost any hero can solo barren you just have to know how he works, most of his dps is in the green stuff that falls from the sky and makes you take more magic damage with each hit, as a caster just use zonah's ring when this happens as a dps, I guess lifsteal it back but know that his basic attack reduces your damage so you hit for about half. while it is possible you prolly shouldn't in short.

karthus...900 ap + lich bane... fastest baron killer ingame :P

I've solo'd baron with Gangplank... I should play that scurvy pirate again someday soon.

Sorry... forgot to list my items.
Youmuu's Ghostblade
Phantom Dancer
Phantom Dancer
Bloodthirster
Infinity Edge
Last Whisper

Seen a warwick with a special build solo him at lvl 13 more than once.

Usually solo it as Nidalee if the game is getting rediculously long, requires blue, CDR cap, and to be reasonably fed, snowballing mejai's shouldn't be too hard along with a Zhonya's and a Ryali's for some extra health and a Lich Bane.