Yes , its possible to do so assuming your hero has good items.
High level runes are almost essential as well, so best to try this once your summoner is at level 30.
Heroes with summons seem to be a good way to solo Nashor; for e.g. Zyra: Shaco: These have the advantage of basically turrets that keep firing at him while you can try to back off and heal.
Other champions who can solo the Baron:
Tryndamere:
Ashe: and well, pretty much any well-fed lvl 18 champion.
gaming.stackexchange.com/users/25150/Alok
The best way to ninja solo Nash safely is with more life steal than you loose
It do it frequently with : Fiddlestick (14)(Blue + 400 AP)
Tryndamere (Good critical +
Bloodthister)
Olaf (Wiggle) Jax(gunblade + Wriggle)
nocturne
(Wriggle)(nahs gives free AS doing spells on the shield ;-) )
Sion (AD + ult)
Xin Xiao(Wriggle)
Nunu jungle with Spirit of the Spectral Wraith and Glacial Shroud + Blue Solo Nashor at 15-20 mn maxing
Q
you just need someone to take some hits for you Think a Nunu
+
Vayne//Kog can do it pretty fast too ;-) Good luck trying that.
Be careful to not be warded and that the other jungler is always visible.
Giving a free nash on a ninja nash is pretty ugly.
gaming.stackexchange.com/users/27063/Hystic
I guessed its mostly AD champions that will be able to solo Baron, even if they are AD champions, they must fulfil two requirements (at least i believed) 1) farmed adequately enough for good powerful items (e.g The Bloodthirster, Black Cleaver ..) 2)
the abilities of the champions, I have tried Xin Zhao before and with his passive ability to gain life and his increase attack speed he is able to match the dmg output of Baron by stealing back some life.
Others I have tried without much success.
The best mix for a solo will be good items and abilities that can either stun or increased attack speed
( XZ seems to have both, the triple strike and his increased attack speed) .
As most tanker champions can't deal out much dmg and even tanker heroes cant tank that long against baron.
gaming.stackexchange.com/users/30570/jonleech
I would imagine that any AD champion with at least 1.0 attack speed and 6 farmed Bloodthirsters should be able to solo Baron, but most builds that you'll see in actual gameplay won't be suitable for soloing him.
Duoing is another story.
gaming.stackexchange.com/users/30428/Kaslai
AP Carrys with spammable spells (cassio, karthus, Ryze, Zyra) have an easy time soloing Baron.
Bruisers/ADCarrys can do so, but its somwhat harder due to Baron Nashor debuffing the AD of the champ who tanks his attacks.
Jax is a really good champ for soloing Nashor.
gaming.stackexchange.com/users/29368/Jacimovski
I have solo'd Baron before with Karthus.
His Defile is the key, of course.
gaming.stackexchange.com/users/30684/Sterling Bourne
Pretty much any character would be able to do this with enough damage and tankiness, but as others have said, the practicality is the real question.
In a custom with a full build and no enemies to stop you, Baron is not that difficult for any champion (with some exceptions).
However, in a real game you have to finish Baron before the enemy team catches wind of it, so the list is very much smaller.
As far as I know there is no comprehensive list of characters who can do it, but I imagine it is most of the characters in league with the right build.
gaming.stackexchange.com/users/31163/Kevin Wells
Actually ADs have a slight problem with killing Nashor, because Nashor have a debuff called Voracious Corrosion which lowers AD by 50%.
He uses it if he takes major physical damage.
Still with enough AD and lifesteal the ADC can beat him.
Champions like Jax or Fiddle is better since they have possibility of spellvamp instead, which Nashor is weaker against.
gaming.stackexchange.com/users/42396/Wertilq
Yea I've done it with Jax multiple times.
It's all about the gear you get, having life steal items and some other powerful items makes it relatively easy with jax.
gaming.stackexchange.com/users/44262/ZOMGitsLogan
Warwick can take him down alone very fast.
The build I use to do this is:Zephyr, Phantom Dancer, Berserker's Greaves, Spirit Visage, Warmog's Armor, and Wriggle's Lantern (or Wriggle's situational replacement) Almost full health when done with him.
gaming.stackexchange.com/users/48614/Master Magus
Is it possible to solo Baron Nashor?  Are any champions able to solo Baron Nashor, and if so what champions can do so?  To try to make this a better question, I was inquiring more late game under normal game circumstances if any champion could solo Baron Nashor. I was more concerned of us having 4 champions in view and having one of their enemy champions "ninja" baron while we are preoccupied fighting the rest of their team.
Is it possible to solo Baron Nashor?
gaming.stackexchange.com
<league-of-legends>
gaming.stackexchange.com/questions/79929
gaming.stackexchange.com/users/18697/Halfwarr
There is no list of characters who can do this. Your hero must have good items. The best mix would be items and abilities than can stun or increase attack speed. While it seems like a hard task, killing Baron solo is doable, but champion and build has to considered, beforehand.
It is mentioned that it is possible to solo Baron.