Milestones in Brain Development
Encyclopaedia Britannica video on the basic developmental stages of human life

How Baby Brains Develop
CNN summary on the topic

Insight Into the Teenage Brain
TEDxYouth video on the topic

Synaptic Pruning, Animation
Alila Medical Media video the topic

You can grow new brain cells. Here is how.
Sandrine Thuret TED-Talk on neurogenesis

2-Minute Neuroscience: Myelin
Neuroscientifically Challenged video on the topic

Romania's Last Orphanages
The Economist video on the topic

Piaget's Theory of Cognitive Development
Sprouts video on the topic

Object Permanance at 6 and 13 months of age (Sensorimotor stage)
An example video on the topic

Three mountain task (Pre-operational stage)
An example of Piaget's task on egocentrism

A Typical Child on Piaget's Conservation Tasks (Pre-operational stage) 
An example video on the topic

8 Stages of Development by Erik Erikson
Sprouts video on the topic

Theory of Mind
BrainFacts.org video on the topic

Roxanne - Private Speech
An example video of Vygotsky's private speech

Girl toys vs boy toys: The experiment
BBC Stories video on gender learning gender roles

Bobo doll experiment (1961)
Summary of the famous experiment with explanations from Albert Bandura

The Bobo Beatdown
Crash Course Psychology summary of the bobo doll experiment and related matters

Study: quality recess crucial for children
KGW news video on the topic

Designing playgrounds for happier, healthier kids
TEDx talk on the topic

Adolescent risk-takers: the power of peers
Nature video on the topic

Konrad Lorenz experiment with geese
juancarlosboeda video on imprinting

Harry Harlow's studies on depency in monkeys
Michael Baker video on the topic

Mary Ainsworth's strange situations and attachment styles
Psychology Unlocked video on the topic

How poverty affects children's development
Humanfactoids video on the topic

Epigenetics
TED-Ed video on the topic