The Penguin, the Riddler, and Catwoman are perfect for the Nolanverse.
Completely normal people, save for their monomanias. No superpowers. No weird deformities (normally - sometimes the Burton Penguin reappears).
*Penguin *- overweight crime lord with a penchant for formal wear, and an obsession with birds and umbrellas.
Riddler - a brilliant man who loves puzzles, and indulges himself by pitting himself against the cops and the Batman in a riddle-based battle of wits.
Catwoman - a burglar with a cat obsession, and a crush on Batman.
Other Batman villains who work without major problems:
Victor Zsasz - his self-mutilation is a little unusual, but not really weird.
Hugo Strange - ignore his first few appearances, and concentrate on his obsession with Batman’s civilian identity, and his manipulative psychological tricks.
Black Mask - revert to the original, where the mask was really a mask, or use the current version, where the Black Mask is an MPD case manipulated by Strange. The mask-as-face could even work, if played right.
Some who are workable with minor alterations:
Poison Ivy - get rid of the poison blood, and the plant manipulation, have her use plant-based drugs and poisons, delivered by lipstick, to make men pliable, or kill them.
Bane - get rid of the Venom (maybe replace it with steroids or a stimulant), tone down his strength level, and redesign his costume a bit, and you’re golden. The stimulant version even allows a variant on the trick Batman typically used against Bane when he was using Venom - in the original, he cut off the Venom supply, with a stimulant, he could induce an overdose.
Clayface - Go with the Karlo version, who was simply a master of disguise. No actual shapeshifting, engulfing people, or melting people. In this category only because those that are familiar with him are generally more familiar with the later, powered, versions - primarily Hagen.
Firefly - get rid of the flying, make his costume a bit bulkier to allow for larger tanks of incendiary material, and he’s a simple costumed arsonist.
Calculator - go with the recent version of an information-broker to the underworld.
Some who could work without major alterations, if played right:
Mad Hatter - his mind control devices aren’t really far out in relation to Ra’s’s microwave device from the first one. Maybe make them a bit bigger.
Killer Croc - Don’t go with the actual crocodilian version, and depending how the makeup is done, his scaling could be realistic, but still evoke crocodiles.
Ventriloquist - a fairly daft gimmick, but it has the potential to work, even in the grittier Nolanverse - just don’t play the ‘is Scarface real?’ card.
Wouldn’t work, or would be the character in name only:
Mr Freeze, Man-Bat, The Clock King, (all powered to the point that toning them down would make them completely not the same character),* The Condiment King* (no way to not make him ridiculous), Killer Moth (the only way anybody’s managed to make him not-ridiculous makes him not nearly realistic enough).
Not at all a comprehensive list of Batman villains, or even the ones I know and like - just the ones I have strong ideas on how they’d fit into the Nolanverse.