Gibbering Genius

When the only person who gets to speak with realistic diction is the brilliant but quirky scientist. Maybe you want to show that the character in question thinks so fast they they have to Motor Mouth to try to keep up. To be less charitable to the actors and writers, maybe it's what perfectly sensible Clever Stuff sounds like when you don't understand most of the words.

This character may also use characteristic phrases of Buffy Speak. The reason that most characters don't speak like this is because Realistic Diction Is Unrealistic.

If they're using a lot of big words, it's Sesquipedalian Loquaciousness. If they're tossing out swear words or slang just as frequently, they're Sophisticated As Hell. The opposite of this, where a character speaks in highly-calculated terms, is Spock Speak.

Actors

 * Jeff Goldblum has this as his Characteristic Trope. It's easier to list the films where he doesn't do this:
 * The Life Aquatic
 * Earth Girls Are Easy arguably because he doesn't have much dialogue.

Live Action TV

 * Daniel Faraday on Lost.
 * Abby Sciuto on NCIS has a serious case of motor-mouth.
 * Phoebe's scientist boyfriend David (played by Hank Azaria) on Friends.
 * Ross, the most intellectual member of the main cast, also tends towards this (and is mocked mercilessly for it).
 * On Doctor Who, The Tenth and Eleventh Doctors both do this a lot. Ten is more of the gibbery type, while Eleven does a variant where he very calmly rattles off his thoughts as he goes, with the occasional apparent non-sequitur thrown in.
 * The First Doctor tended to do this, especially when William Hartnell, who was getting on in years, forgot his lines and had to adlib.
 * Arguably Murdock from The A-Team. Much of his craziness is laced with some genuinely brilliant stuff. He frequently gets the rest of the team out of tight spots by singlehandedly performing impossible rescues, and all the while he's babbling on unintelligibly.....and not always in English.
 * Gaius Baltar of the Battlestar Galactica remake. The Sanity Slippage didn't help.
 * Many characters on AMC's Rubicon, especially Will, Miles, and Ed.
 * Ladies and Gentlemen, from Criminal Minds, may I present to you, Dr. Spencer Reid and his amazing rapid-fire statistics! Generally, though, he has a bit of a stammer in his speech when he tries to be social, like talking to a girl.
 * Dr. Daniel Jackson of Stargate SG 1. This is Lampshaded in the pilot to Stargate Atlantis when Daniel is starting to explain something to Jack, and Jack asks if this is the part where Daniel gets excited and starts talking real fast.
 * In Stargate Atlantis, Dr. Rodney McKay is prone to this, being an Insufferable Genius.

TabletopRPGs

 * In Genius: The Transgression, higher Inspiration (i.e. stronger mad science) has a detriment in the form of Jabir, an effect that makes it harder for Geniuses to talk to mere mortals or even fellow Geniuses.

Video Games

 * Professor Mordin Solus does this constantly in Mass Effect 2 to the point where, at times, the player is given the option to interrupt him.
 * Two PARAGON interrupts (and a Renegade one) in his first appearance.
 * This then carries over to Mass Effect 3 when his patient calls him out on it, due to his rambling tendencies interfering with her sleep.
 * Johnny Powell, the not-all-together supernatural expert in The Darkness 2.

Western Animation

 * Delbert in Treasure Planet is an astrophysicist and constantly stammers. Considering he's played by David Hyde Pierce that's unsurprising, though (apparently the role was written for him).