Along the lines of “she sells sea shells by the sea shore.”
Examples in your (or someone else’s) native language (not English)?
Dutch: De kat krabt de krullen van de trap met drie droge doeken.
Afrikaans: My liewe neef Louw, my neus jeuk nou. Jeuk my liewe neef Louw se neus ook nou?
German:Fischer Fritz ißt feine frische Fische, feine frische Fische ißt Fischer Fritz.
Here’s an example Thai tongue-twister:
ยายกินลำไย น้ำลายยายไหลย้อย … /yai kin lamyai namlai yai lai yoi/ … The meaning is ‘Grandma eats longan, Grandma’s saliva drools.’
Wenn du denkst du denkst dann denkst du nur du denkst
Spanish: “Tres triste tigres trabajan trigo.”
“Three sad tigers work wheat.”
My elementary school French and German classes primarily comprised songs and rhymes. The only one I remember well enough to look up:
Bonjour Madame Sans-Souci.
Combien sont ces soucis-ci?
Six sous, ces soucis-ci.
Six sous?! C’est trop cher, Madame Sans-Souci.
Swedish. There’s lots of variants of this one, but this is the most amusing one I found online:
Depending on where in the country you are from, the sj/sk sound is a bit like “sh” or “hwu”.
Como poco coco cómo, poco coco compro.
There’s the Japanese one: “Sumomo mo momo, momo mo momo, sumomo mo momo mo momo no uchi”, meaning, “Plums are peaches, and peaches are peaches, and plums and peaches are both types of peaches.”
I know it as tragan (swallow, eat) or trillan (thresh). Any of the three versions makes for some very sad tigers indeed 
I found a whole website dedicated to short tongue-twisters in Spanish and English. And here you can see some in Catalan.
There’s a Catalan one I had to learn for Christmas when I was little, which isn’t in that page and apparently has as many variations as speakers, with the first line being the part everybody agrees on. This is the version I got from my family:
setze jutges d’un jutjat mentgen fetge d’un penjat (16 judges from a tribunal eat a hanged man’s liver)
si el penjat es despenjés, setze jutges ja no en mentjarian mai el fetge d’un penjat (if the hanged man unhung himself, the 16 judges would never again eat a hanged man’s liver)
In Finnish: “hisi sihisi hissa” (A devil hissed in an elevator.) You should have no trouble using this in every-day conversation.
Hebrew: “Sarah shara shir same’ach” (Sarah sings a happy song).
Slovenian: “Pešci, ščistite cestišče” (Pedestrians, clean out the road).
It’s “hiisi sihisi hississä”, actually. Pretty easy to say.
There’s also “mustan kissan paksut posket” (black cat’s thick cheeks) which is a bit harder, especially if you try to say it a few times in a row. And “pappilan apupapin pankolla papupata porisee” (bean dish boils on assistant priest’s clergy house oven).
Not my native tongue, but in French “If six saws saw six sausages, six hundred and six saws saw six hundred and six sausages”:
Si six scies scient six saucissons, six cent six scies scient six cent six saucissons
Me no speakee Basque, but I do know how to use the Basque-Spanish dictionary
The top half is “magic formulas”, the bottom half is tongue-twisters.
And more tongue-twisters.
Pronounced:
“BorkBorkBörk.BorkBorkBörkBorkBorkBörkBörkBorkBörk,BorkBorkBörkBorkBörkBork.”
As I eat little coconut, I buy little coconut (Please mentally delete that tilde that doesn’t belong there).
Another one: Pepe Pecas pica papas con un pico.
Translation: Pepe Pecas chops potatoes with a pickaxe.