Explore Nature with them, go for long walks in the forest, put on wellies, walk through streams and experience a whole new world.
Fly kites.
Go cycling and roller-blading by the river.
Bake cakes and cookies with them, let them lick the spoon, the bowl and get chocolate and dough all over their faces.
Make pizza with them and let them choose the ingredients.
Answer their questions about The Facts Of Life and don't be offended when they get bored and ask if there are any biscuits left in the tin.
Read 'Winnie Ther Poo" to them, do all the voices and try not to wet your knickers, laughing.
Read them 'Ayn Bylton's' (Enid Blyton's) Famous Five stories and try not to be snarky about those pompous kids.
Plough through the Harry Potter books, revel in The Hobbit and breathe a sigh of relief when they are old enough to read "The Lord of the Rings" by themselves.
Laugh with them at "The Simpsons, South Park, Scrubs ..." and try not to scream and gag during "Game of Thrones".
Try to keep a straight face when your 14-year-old son tells you what a vibrator is and that it's designed for men! (Or is there something I should know?).
Sit up with them all night when they're little and unable to sleep because of a bad cough, tummy-ache, some childhood malady.
Entertain them with shadow-puppet shows when you're propped-up in bed with migraine and their dad 'can't cope' any more.
Lie in the dentist's chair with them on your lap and hold their hand while they're getting a filling. 
Stand up to their teachers when they are being unreasonable (the teachers). Try not to laugh when an outraged teacher calls, on a hot summer day, to request that you pick your son up from school because he is dripping wet, having "fallen into the swimming pool, fully-clothed, and he might catch a cold!???!". (Failed, miserably on that one!).
Don't tell your son that you know he jumped in to impress his friends, or that you did something similar at his age - to impress a Boy.
Tell them that the puppy fat will disappear soon enough and that girls WILL fancy them before too long.

Let them have days off from school, just for the sake of it.

Get up at 3 am and pick them up, freezing, drunk, or freezing AND drunk after a party and unable to get a taxi.
Drive their friends home through snow and icy streets, because their parents refuse to come leave their warm beds to pick them up.
Send your 'boyfriend' home, just when things are getting interesting, in response to a phone-call at 10 pm, informing you that your son is blind drunk and thinks he is going to die.
Place son in your new car, with the help of several strong young men, and drive him home, holding his head out of the window so that he doesn't puke over the upholstery.
Call said 'boyfriend' and drag him out of bed to come and help get drunken, leaden son out of the car and into bed.
Refrain from telling them how unfunny their drunken, repeated jokes are, especially at 3 o'clock in the morning and encourage them to go to bed and sleep it off. Promise them pancakes in the morning.
Never let-on if you don't like their friends and, later, girlfriends.
Welcome their friends into your home, even if they give you goose-bumps.
Admit to them that you were wrong and APOLOGISE (but don't grovel).
Let them know that you are not perfect.
Listen, with interest, to their music, even if it's not to your taste.
Listen, without comment, when they complain about the girlfriend you don't like. 
Try not to enthuse too much about the girlfriends you do like unless you are absolutely sure they are going to marry them. 
Try not to embarress them in front of their friends (impossible!). 
Don't fuss when they end up in hospital with alcohol poisoning or when you have to collect them from the local police station in the wee hours of the morning. 
Tell the police that, of course, you will punish them severely, then take them out for an ice-cream or a drink (depending on their age) and have a gentle chat about things. Don't panic when they show up at school (the one where you happen to be a teacher) stoned, or disturb you in the middle of a lesson to tell you that their girlfriend is pregnant.
Don't bore them with tales of your childhood and youth-hood, unless they really want to hear them. 
When they are pissed-off with you and go and live with their dad and don't contact you for weeks, or months, let them be and give them the space to come back in their own sweet time. 
When they do return, don't grovel with gratitude and do their laundry for them! 

When they tell you that they want to become Buddhist, convert to Islam, have become Atheists just say: "Alright, darling. That sounds interesting".

Tell them you still love your ex-husband (their dad) even if you feel like kicking him and his balls to the moon!

Let them know that you love them and will always be there for them, but don't love them too much and let them walk over you.
Don't try to be their 'friend'. They will have friends-a-plenty, but they only have two parents.
Don't try to clip their burgeoning wings when they start peeking over the edge of the nest. 
Shed a private tear, let them fly, then pour yourself a glass of good wine and light up a cigarette (should you be so inclined). Pump up the volume, dance to YOUR music and look forward to the time when they come to visit as young adults, perhaps bringing 'wives' and grandchildren.

Ah! Grandchildren:

'Explore Nature with them, go for long walks in the forest ...'