I think the 4/5 Chillwind Yeti and the 6/7 Boulderfist Ogre are the only completely textless (and typeless) cards that're favoured in arena and/or played in viable constructed decks, and the Ogre is only really played in budget constructed stuff or the arena.
The Chillwind Yeti hits a lot of awesome sweet spots that make it an extremely good card in a huge number of decks: at 4/5 for 4 mana, it will trade 2 for 1 with every single minion that could've been cast on an earlier turn (3 or less mana) except the Magma Rager and Scarlet Crusader, and the majority of minions that could be cast on the same turn (4 mana); with 5 health it's not cleared by Flamestrike or Swipe, so is good against Mage and Druid; and with 4 attack, it's not cleared by Shadow Word Death or Shadow Word Pain, so is excellent against Priest*. And yet it's not a 'big threat', so often players won't spend their premium hard removal (polymorph, assassinate, hex, &c.) on it, and if they do you're not too upset, because that's a removal spell they can't use on your really big guys.
I can't actually think of any other textless, typeless cards, offhand. After a quick search, there are 3 others: Wisp (1/1 is frequently free to remove and rarely has an impact, so is basically instant card disadvantage in almost all decks), Magma Rager (5/1, again the 1 health makes it basically free to remove, or at least easy to find a beneficial trade, for the majority of opponents), War Golem (7/7 is fine, but the Boulderfist Ogre is basically just as good for the role at 6/7 for one less mana).
*My favourite thing to do against control-ish Priest players is to find a way to get a load of 4 attack minions down, so the Priest's best removal cards are all dead.
EDIT (because otherwise double post): This Paladin arena
was pretty crazy. Almost nothing but Hunters and Paladins - fortunately my deck was excellent against most Hunters, because I had two Guardian of Kings for lifegain and two Avenging Wraths for board clear. I probably missed a win somewhere - the final game against the Mage was pretty close.