I have no children, but I do have a niece, as of about a month ago, so I'm going to answer this anyway.
Bagpuss. It somehow just feels so cosy and safe while being inventive enough and with enough variety in the episodes to be enjoyable even now. Mostly it's just nostalgia - Oliver Postgate's voice just evokes childhood - but hopefully a toad with a banjo could appeal to even the jaded youth of today.
Supplement from 04/20/2008 12:05am:
I'd forgotten how weirdly melancholy the opening sequence was.
So so many.
First love was probably Bod. (Here comes Bod. [cue intro music]) Hooks you right in from the start. For a very young spangle this was the centre of my universe. Loved that cartoon and all those strange noises.
Must mention many some of my other favourites: Henry's Cat, Battle of The Planets, The Kids of Degrassi Street, The Red Hand Gang, Dungeons and Dragons, Around the World in 80 Days....