I wanted to kick this article off with a few in the "best" category, but I really only have one, and that's only because I read it on this guy's blog.  Please share yours ;).

That said, I have many, many, MANY for the Worst category!  Alternatively, if the key demographic for these jokes are two-year-olds, in the words of the immortal Kenny Bania...

gifirific.com

1. Why can't you tell secrets on a farm?  Because potatoes have eyes, and corn have ears.

2. What do you say to an angry 300-pound baked potato? Anything, just butter him up.

3. “I think,” said the sweet potato, “Therefore I yam.”

 

The One Good Potato Joke In Existence

One night, the Potato family sat down to dinner–Mother Potato and her three daughters. Midway through the meal, the eldest daughter spoke up. “Mother Potato?” she said. “I have an announcement to make.”

“And what might that be?” said Mother, seeing the obvious excitement in her eldest daughter’s eyes.

“Well,” replied the daughter, with a proud but sheepish grin, “I’m getting married!”

The other daughters squealed with surprise as Mother Potato exclaimed, “Married! That’s wonderful! And who are you marrying, Eldest daughter?”

“I’m marrying a Russet!”

“A Russet!” replied Mother Potato with pride.

“Oh, a Russet is a fine tater, a fine tater indeed!”

As the family shared in the eldest daughter’s joy, the middle daughter spoke up. “Mother? I, too, have an announcement.”

“And what might that be?” encouraged Mother Potato.

Not knowing quite how to begin, the middle daughter paused, then said with conviction, “I, too, am getting married!”

“You, too!” Mother Potato said with joy. “That’s wonderful! Twice the good news in one evening! And who are you marrying, Middle Daughter?”

“I’m marrying an Idaho!” beamed the middle daughter.

“An Idaho!” said Mother Potato with joy. “Oh, an Idaho is a fine tater, a fine tater indeed!”

Once again, the room came alive with laughter and excited plan for the future, when the youngest Potato daughter interrupted. “Mother? Mother Potato? Um, I, too, have an announcement to make.”

“Yes?” said Mother Potato with great anticipation.

“Well,” began the youngest Potato daughter with the same sheepish grin as her eldest sister before her, “I hope this doesn’t come as a shock to you, but I am getting married, as well!”

“Really?” said Mother Potato with sincere excitement. “All of my lovely daughters married! What wonderful news! And who, pray tell, are you marrying, Youngest Daughter?”

“I’m marrying Peter Jennings!”

“Peter Jennings?!” Mother Potato scowled suddenly. “But he’s just a common tater!”