Worms are invertebrates with elongated, soft bodies. Though the earthworm is the most common, there are many varieties of worms, who in popular culture often have negative connotations, associated with "creepy crawlies" at worst, or with sour-flavored gummy candies at best. On Sesame Street, however, the worm is a much loved and vital species with an elaborate culture and society of its own.
Worms have appeared on Sesame Street as early as the first episode, in an animated segment to demonstrate the letter W. Early segments of this often referred to the worm as "yucky," feeding to the popular prejudice, and raising concerns from one conservationist. 
For the most part, however, worms are presented in a very positive light, mostly in the person of Slimey the Worm, pet of Oscar the Grouch. Slimey is beloved by Oscar, well-liked by other residents, and proved popular with viewers; in a 1971 pet show episode, tests showed that children "were attentive, responsive, and loved Slimey the Worm." Later, Slimey's family was introduced, including baby sister Sloppy, parents Dusty and Eartha, and cousins Squirmy and Rachel.
Not unlike the Twiddlebugs, worms have their own community, culture, and organizations, established through the labor of the worms themselves. They establish their own mass transit system in the form of a worm subway (Episode 3164) and band together to build a playground (Episode 3957). In addition, Slimey is a member of the Worm Scouts, a scouting troop, and all worms enjoy the annual Wormy Gras festival, the annelids' answer to Mardi Gras, and an ode to the joys of worminess.
The worms also benefit from more elaborate organizations and events, many of which which are open to worms across the globe, not just those in and around Sesame Street, which were explored in detail in multiple episodes. The worms have their own version of the Olympic Games, the Worm Games, held in both summer (Episode 3300) and winter. To prove that it's not all fun and games for worms, WASA, the Worm Air Space Organization, furthers space exploration and scientific discovery through the use of manned worm missions; the progress of one international team of worms (including Slimey) was tracked through much of Season 29. As demonstrated in Worms in Space segments, the crew took time from their mission for educational pursuits, forming letters with their bodies.
On The Muppet Show, two slightly different inchworms were featured during Charles Aznavour and Danny Kaye's versions of the song "The Inch Worm." Two striped worms more similar to those seen on Sesame Street appeared in "The Glow-Worm" sketch on Muppet Show episode 204.