While most Muppets are timeless characters who don't age, occasionally younger versions are seen in flashbacks and older versions are seen in fantasy visions of the future.
Infant versions of several classic Muppet characters appeared in a fantasy sequence in The Muppets Take Manhattan. The "babyfication" of the characters continued in the Muppet Babies animated series (and it's 2018 reboot) along with related merchandise and tie-ins. Adolescent versions of the characters (somewhat based on their Muppet Babies personas) appeared in illustrated form in the Muppet Kids series of books in the 1990s, depicting the characters as pre-teens. Kermit's adolescences was explored in the 2002 direct-to-video movie Kermit's Swamp Years, showing a younger Kermit (along with a cameo of younger versions of Statler and Waldorf).
Following in the footsteps of the Muppet Babies, infant versions of the Sesame Street characters also began to appear in merchandise and books starting in the late 1980s. A series of Toddler Books was published between 1987 and 1992 featuring the Muppet characters illustrated as toddlers and given names like "Little Ernie" and "Little Bert." In 1992 a collection of Sesame Street Babies merchandise was produced featuring photo puppets of baby versions of Big Bird, Bert, Ernie, Cookie Monster and Prairie Dawn; illustrated versions of additional characters were also included in the series of books. In 2006 a series of home videos entitled Sesame Beginnings was produced featuring puppet versions of Baby Elmo, Baby Big Bird, Baby Cookie Monster, and Baby Prairie Dawn; the infant Elmo and Cookie Monster puppets would later appear in other videos and episodes during flashbacks to the character's childhoods. Illustrated versions of Sesame Street characters as babies continued to appear in a series of Sesame Beginnings books; plus the March 2011 issue of Sesame Street Magazine, in multiple doll forms (including a Tickle Baby Elmo doll), and on a variety baby merchandise (including bibs, onesies, diapers, and other baby supplies).
The Muppets
Animal
Beaker
Bean Bunny
see Bean Bunny's Alternate Identities and Ages
Bunsen Honeydew
Fozzie Bear
see Fozzie Bear's Alternate Ages
Gonzo
Janice
Kermit the Frog
see Kermit the Frog's Alternate Ages
Miss Piggy
see Miss Piggy's Alternate Ages
Robin the Frog
Rowlf the Dog
see Rowlf the Dog's Alternate Ages
Sam the Eagle
Scooter
Skeeter
Statler and Waldorf
see Statler and Waldorf's Alternate Identities and Ages
Other Muppets
Human characters
Sesame Street
Bert
Big Bird
Cookie Monster
Count von Count
Elmo
Ernie
Grover
Herry Monster
Oscar the Grouch
Prairie Dawn
Mr. Snuffleupagus
Telly Monster
Other Sesame Street Muppets
Humans of Sesame Street
Fraggle Rock