Children

Children and pregnancies are both regular topics on Lost.

Occurrences

Megan Pace was playing in the backyard when Charlie visited Liam. ("The Moth")
Sawyer aborted a con after he saw a boy that reminded him of his past. ("Confidence Man")
Aaron Littleton was kidnapped in utero, along with his mother. ("Raised by Another")
An unborn baby was lost after Christian Shephard accidentally killed Beth while operating on her drunk. ("All the Best Cowboys Have Daddy Issues")
Shannon spent a year in Paris watching a child named Laurent. That's when she learned the song that helped Sayid understand the maps he took from Rousseau. ("Whatever the Case May Be")
Aaron Littleton's mother, Claire, escaped Ethan Rom. ("Special")
Jin threatens to beat up Byung Han in front of his daughter. ("...In Translation")
A kid talked to Locke about Mousetrap in a toy store ("Deus Ex Machina").
Aaron Littleton was born. ("Do No Harm")
Alex Rousseau was kidnapped as a baby, and raised by the Others. ("Exodus, Part 1")

The poor man's son needed to go to the bathroom. ("...And Found")
Sophie was cared for by Shannon for a year. ("Abandoned")
Zach and Emma were both taken by the Others. ("The Other 48 Days")
Ana Lucia's unborn baby was lost after she was shot. ("Collision")
Charlie has a flashback in which he and his band play in a big child's crib for a commercial. ("Fire + Water")
Sun was confirmed as pregnant. ("The Whole Truth")
Christian Shephard demanded to see his daughter. ("Two for the Road")
Charlotte Malkin's "death" and "miraculous revival" summoned Mr. Eko to investigate on behalf of the Catholic Church. ("?")

Karl was shown as a teenaged boy imprisoned by the Others. ("A Tale of Two Cities")
Bobby was a boy living in the commune. ("Further Instructions")
A picture of Clementine Phillips was shown to Sawyer while Sawyer was in prison. ("Every Man for Himself")
Daniel asked Mr. Eko "Are you a bad man? My mother says you are a bad man." ("The Cost of Living")
Juliet is revealed to be a fertility doctor. She has impregnated a male field mouse and successfully uses a new drug to make her sister fertile. Dr. Alpert asks her to examine the CT scan of an unusual womb. ("Not in Portland")
While staying in Phuket a young Thai boy sold Jack sodas on the beach. ("Stranger in a Strange Land")
The children kidnapped by the Others, Emma and Zach, are seen at the Hydra station under the care of Cindy. ("Stranger in a Strange Land")
Zach and Emma are later seen again with the Others at the ruins. ("The Brig")

Emma and Zach are seen again inside the Temple. ("LA X, Part 2")
There are also two other children seen living at the Temple, one of them a young boy and the other a girl around Zach's age. ("LA X, Part 2")
Jacob and the Man in Black are seen both as new-borns and teenagers. They are also revealed to be twins. ("Across the Sea")

Many characters have had flashbacks that feature themselves as children, and some like Charlotte have been seen as children on the Island's flashes:

A young Jack Shephard talks to his father about being beaten up at school. ("White Rabbit")
Young Sawyer is seen talking to his mother. ("Outlaws")
Young Kate's voice is heard on a tape. ("Born to Run")

Younger versions of Eko and his brother Yemi are first seen. ("The 23rd Psalm").
Younger versions of Charlie and his brother Liam are seen at Christmas time. ("Fire + Water")

Young Sun-Hwa Paik is seen in the opening scene of the episode. ("The Glass Ballerina").
A young Eko is seen again with a younger Yemi. ("The Cost of Living")
A young Hurley Reyes is seen talking to his father. ("Tricia Tanaka Is Dead")
Young Ben arrives on the Island with his father. ("The Man Behind the Curtain")
Young Charlie is taught how to swim at Butlins by his father. ("Greatest Hits")

An infant Locke is born, and at age 5, is visited by Richard Alpert. ("Cabin Fever")

A young Charlotte is seen and recognized by Daniel Faraday. ("LaFleur")
A young Sayid is seen in Sayid's flashbacks. ("He's Our You")
A young Miles is seen in Miles' flashbacks. ("Some Like It Hoth")
A young Daniel is seen in Daniel's flashbacks. ("The Variable")
A young Charlotte is instructed by Faraday to leave the Island, ("The Variable") and leaves the Island on the Galaga. ("Follow the Leader")
A young Juliet, Sawyer and Kate are seen in flashbacks. ("The Incident, Part 1")

Some characters have had flashbacks that feature themselves as teenagers:

Although she is not seen as a teenager, Kate has a flashback which contains her and her childhood sweat heart, Tom Brennan listening to a tape recorder which contained an entry of Kate and Tom as teenagers (around 12-13 years old). ("Born to Run")

One of Locke's flashbacks takes place while he is attending high school and living with his foster parents. ("Cabin Fever")

Both Eloise Hawking and Charles Widmore are seen at the age of 17 in 1954. ("The Lie") ("Jughead")
Ben encounters multiple main characters as 12-year-old living with the DHARMA initiative in 1977. ("Namaste") ("He's Our You") ("Whatever Happened, Happened") Later, Ben has a flashback to his time with the Hostiles as a 12-year-old as he healed from a gunshot wound. ("Dead Is Dead")
A teenage Miles visits his dying mother. ("Some Like It Hoth")

Both Jacob and The Man in Black are depicted as 13-year-olds in their flashbacks. ("Across the Sea")
Teenage Jacob previously appeared as a vision to the Man in Black, Sawyer and Desmond. ("The Substitute") ("Everybody Loves Hugo")

Pierre Chang feeds baby Miles before going to work. ("Because You Left")
Baby Ethan is born to Amy and Horace, with a help from Juliet who is shocked by this fact. ("Namaste")
Ben remembers the day he stole a one week old Alex. ("Dead Is Dead")

A flashback shows the birth of both Jacob and the Man in Black. ("Across the Sea")