Playing as Children?

I finally came up with this (I use 4e): Child characters are one size smaller than adults, until they are around 13/14, when they assume adult size. Characters who already belong to a Small race (i.e. halflings) do not become Tiny! Stats for each character should be rolled as usual, but disallowing any stats that would be ludicrously high given the character's age (i.e. no 9-yr-olds with Strength 18!) Natually, opinions will vary as to certain issues such as how wise or intelligent children can be, since some people believe that wisdom only comes with age and others believe it is inate. It's up to the Players and the Dm to decide if they want realistic children or allow for child prodigies. (The Barbarian kid Bobby from the old Dungeons and Dragons cartoon clearly had greater strength than realisticly possible for a boy his age... if that's what you want, go for it.)

^^Correct. OTOH, some players might find it creepy to have a little kid with an adult mind. One common theme you see in fiction is the son or daughter of a character whose mind has been overtaken completely or is a reincarnation of their father. Their father now seeks revenge against those who murdered him while his wife was still pregnant with said child.
A variation is an ep of the Ghost in the Shell anime series where a 16yo son acquires the cyberized memories of his father (a notorious assassin who himself was assassinated) and his mind becomes melded with that of his father. This leads to problems because the son's impulsiveness leads to hatred and recklessness towards the enemies of his father (whereas the father was a calm, cool professional)

A similar example is the Avatar cartoon series, though the ancestors of the protagonist are not assassins by trade nor are they motivated by vengeance.

Nonetheless, the common theme in all of the examples I've given is a child's innocence and immaturity contrasting with an adult's temperance and mercilessness towards his or her enemies.

If desired, I could post all the rules for child characters I've seen so far - I wrote them down on a piece of paper once. This would include the rules from the Ist d20 edition of Star Wars (presumably added since the film Phantom Menace starred a 9-yr old Anakin Skywalker - later editions dropped the
rule!) As Hyena of Ice stated, there are pretty heavy ability score penalties, but someone might wish
to use them nonetheless (I would only use them if you are also using the score adjustments for aging
that apply to older characters, also.) A penalty to speed is common, too, because children are shorter.

O.k. The Star Wars rules were as follows: Any human character 11 and under is in the "Child" category and has a speed of 6 meters (as opposed to 10 for adults). You take a (total) penalty of -4 to Str and Con, and -2 to all other ability scores. Any character age 12 to 15 is a "Young Adult" with the adult movement rate (10 meters) and -1 to all ability scores (As your character ages, you gradually loose the penalties to scores.)

In D20 Modern, children are only allowed as NPCs and have the following rules: They are aged 11 and younger, have no class or level, and have -3 to Str and Con and -1 to the other scores. They have 1d4 hit points and get no feats or skills, and have a speed of 20 feet.

That's all I have for right now, if I find more rules I'll post 'em.

Also, VikingLegion, as reguards Bobby's high Strength score, I remember looking at the stats for him that were included with the Dungeons and Dragons animated cartoon DVD release, and there I believe they gave him an 18 STR, only four points of which were a bonus from the magic club. In other words, he had a natural 14 STR - pretty impressive for a 8-yr-old! (They also made all the characters Medium size, for what it's worth.)

If your playing 2nd edition the cormanthor book has some adjustments for kids... geared for elves I know but worth looking at.

I don't see any necessary reason why it has to universally be one or the other. It could easily vary from person to person. I imagine it also has a lot to do with what traits exactly the child happens to have; a major difference in physicality's a lot more likely to be something they had from birth than an odd hair color or a strange aura.