The one that gives me the most trouble is simply a name: “Peggy Babcock.” I just can’t say that one more than once without coming out with “Pebby Bagpop” or some such.
RR
Rikki Lake Late
I have a coworker who says “rice mountain” every time she tries to say “right mouse button”
Pheasant plucker.
(as in:
“I’m not a pheasant plucker,
I’m a pheasant plucker’s son,
And I’m only plucking pheasants,
'til the pheasant plucker comes.”)
<Dana Carvey>
Joodishul System!
</Dana Carvey
She showed me sushi
Strange strategic statistics
We had to master that one for high school drama. It’s very tough!
Rikki’s boyfriend worried!
That, and what Lib said. That was one of 5 or 10 “exercises” my drama teacher assigned us for practice. Then she said nothing about it for weeks. Then one day, if you wanted to get into class, you had to pass the test. I drew redleatheryellowleather. Ten times.
I’m also the one she made say the Greek alphabet backwards.
From a contest in Games Magazine:
Cinnamon Synonym.
Brock Blake’s black bike’s back brake bracket block broke!
Right white wheat reapers reap white wheat right.
Also:
United States twin screw cruiser.
The Leith police dismisseth us.
Longlife Lite Ballpoint Pen.
I slit a sheet; a sheet I slit; upon the slitted sheet I sit.
(Sorry, that’s a little longer. :p)
I can’t say the word sixths. I have a hard time even thinking the correct pronunciation.
edited it
(Short)
Vim. Van. Van. Vim.
Black bug’s blood.
Bread, Blessed and Broken.
(Long)
A BIG BLACK BUG BIT A
BIG BLACK BEAR. THE
BIG BLACK BEAR BLED BLUE BLOOD
ALL OVER THE BIG BLACK BARN FLOOR. --in under five seconds.
I can say: Theophilus Siffle, the successful thistle sifter, while sifting a sieve of unsifted thistles, thrust 3000 thistles through the thick of his thumb…see that thou…thrust not 3000 thistles through the thick of thy thumb
–with an “ith” tacked onto each syllable.
One of my classmates read “the liquor locker lackey” for speech class.
(Hard)
The fox’s where *three… free…fleas…flew…through…three…trees…in freezing breeze…and *SNEEZED!
(Very Hard)
dougie’s second one.
I love twongue tisters. 
Ethicists.
W
pool cue
Tai chi, chai tea
You beat me to it. GW and many others have trouble with it. Even Jimmy Carter, who has a degree in nuclear engineering I think, garbles it a little. Maybe that’s because he grew up in Plains, GA.