I am not a fig plucker
Nor a fig plucker’s son,
But I will pluck figs
Until the fig plucker comes!
Try that three times fast!
What’s your favorite?
Susie Shelby sits shining shoes. Susie sit as Shelby shines, and Shelby sits as Susie shines.
Old Mother Rutterputter’s rough-cut punt
Not a punt cut rough, but a rough-cut punt
Hollow in the middle and shaggy in the front
Old Mother Rutterputter’s rough-cut punt
say “unique new york” 5 times fast
Heck, try saying “thistle” five times fast. That’s the worst tongue twister I know.
A slight modification on BrainGluttons 1st one…
I’m not the pheasant plucker, I’m the pheasant pluckers mate
I’m only plucking pheasants cause the pheasant pluckers late
I’m not the pheasant plucker, I’m the pheasant pluckers wife
I’ve been plucking mother pheasants my whole pheasant plucking life
I put my foot in the bucket, and footed the bucket about
I shine my city shoes
She sells seashells by the seashore
Rubber baby buggy bumpers
Any one of those, as fast as you can 5x in a row. Ahh that brings back memories …
The big black bug bled black blood.
Whereat with blade, with bloody blameful blade, he bravely broached his broiling bloody breast. (Not a tongue twister, per se, as it’s from A Midsummer Night’s Dream; however, it certainly tied my tongue in knots the first few times I tried to say it.)
I am a pleasant mother pheasant-plucker.
I am the most pleasant mother pheasant-plucker
That ever plucked a mother pheasant.
“The Leith police dismisseth us.”
Not as good as the rude ones, you pheasant pluckers. 
The sixth sick sheikh’s sixth sheep’s sick. 
(Heck, that was difficult to type…)
I was going to say “Bugs Black Blood” repeated three times, but trying to say your variation just once made me remember my drinking days. You win.
The shotest ones I know:
“Toy Boat” ten times fast.
Or even shorter “oil” ten times fast.
That line is great. 
Actually, you can find all sorts of inadvertent tonguetwisters just by reading Shakespeare aloud – I find, for instance, that “impartial are our eyes and ears” is physically impossible for me to say for some odd reason, and “We are enforced to farm our royal realm” is pretty nasty as well. Clearly I have issues with the letter R (that’s the dog’s name… ;))
This reminds me of that episode of “Pinky and the Brian” with the Hackensack Kicky Sack sack-kicker factory:
From a restaraunt in Florida…named Fudpuckers
How much fud could a fudpucker puck
if a fudpucker could puck fud
Just imagine Pontius Pilate trying to manage those! Or Biggus Dickus doing “Susie and Shelbie sit shining shoes . . .”
A tutor who tooted a flute
Tried to tutor two tutors to toot
Said a tutor who tooted, is it harder to toot
or to tute
or to tutor two tutors to toot?
A diabolically simple one that I always liked…
Say 5 times fast:
Red silk, yellow silk
Jammer
Mrs. Smith’s fish sauce shop.