Having come late to this thread all I can do is to echo many of the previous posters' comments.
Children accept as normal whatever their family does - so our two boys (10 and 13 now) regarded caving, climbing, a great deal of visiting castles (armed with swords, shields, halberds and crossbows), cycling, camping, occasionally working on a steam locomotive, and participating in historical re-enactment events (muskets, cannon and blackpowder period) as normal. 'Show and tell' type sessions and dressing up for World Book Day at school saw them diverging considerably from their peers - but with a lot of street cred from peers and teacher interest for the photos they showed, the objects they took in, and the outfits they dressed up in. Gradually they came to appreciate (in a positive way) how many things they experienced that their peers did not - e.g. the younger boy is currently into the Percy Jackson film and novels and this evening wanted to play at being the Greek god of metalwork - Dad was able to dig out a blacksmith's apron, a small lump hammer, and an anvil. Result: instant satisfaction and yet another comment along the lines of 'Wow! How come you've got all this stuff? None of my friends have the real things to play with' - which enabled me to demonstrate to Mum that it IS worth Dad keeping all that junk in the garage and shed.
Our two started caving at seven years old - the age that they seemed to me to be a suitable height and to have sufficient stamina. However, reading some other posters' anecdotes, suggests that they could have started at a much earlier age. Bernies Cafe caving shop sells good value wet socks, furry suits and oversuits to very small childrens' sizes so you could start early. They grow out of kit fast - it is useful having siblings to cascade the kit to, and friends to sell it on to when its outgrown after a handful of trips. Caving kit is also useful for muddy days in the country or in the garden.
Mum isn't a caver but the elder boy's godfather is, so there has always been two adults to take them underground. Selecting caves with suitable topography is crucial. Equally important is keeping children regularily topped up with food (sandwinches and real food, as well as chocolate etc) and drink when underground. Certainly their having real kit made all the difference to comfort and hence enjoyment and duration of trips. By nine years old the elder boy could enjoy a six hour trip to sump two in Little Neath and a similar length trip to Geoleogy Pot in Giant's.
The younger boy has turned out to be a pretty good and certainly a very enthusiastic climber - at nine he was making credible attempts to second Severes in trainers. Currently he's been promised rock boots if he works hard for his next violin exam. His preference is climbing rather than caving (godfather and dad are rusty but still competent) and it looks like he'll probably forsake caving after he imminently gets his Scouts caving badge as he doesn't like cold water in caves - but loves it on surface in rivers, lakes and beaches. So one child is not a guide to their siblings' prefences.
Neither of our two have yet begun to really enjoy or derive satisfaction from hill walks - as another poster observed, children don't really appreciate views. Our experience suggest keeping walks shorter than adults would necessarily enjoy, and trying for locations where there are aspects to interest children. However, last summer both made it from Pen y Pass to Snowdon summit (in rain) and down the Watkin Path (in sun), spurred on by the presence of their favourite grown-up cousin, age 18.
Children are generally easy to take away for day or weekend or longer trips when they are infants as they sleep most of the time and if you use cold water type sterlising regieme, their stuff is easy to move and set up afresh. The arkward stage comes when they have a voice to complain about being bored and needing the loo, and have stopped sleeping for the greater proportion of long journeys. There then follows a few years when the car has to stop about once an hour for them to run around, widdle, and work off energy. Flights can be horrendous with toddlers. Sanity returns when they are old enough to enjoy story CDs on a Walkman (hint: public libraries usually stock a lot of childens' books on CD) and to read on long journeys.
A baby carrier (front sling type) iss great for walks when they still sleep most of the time - but they can easily get cold / hot / sunburnt so have a care. From about 9 or 12 months, ruucksack-type back carriers are wonderful - they really appreciate the elevated vantage point; they can still get too hot / cold / sunburnt so still have care. Ours were lugged along long distance paths in back carriers on long day walks perfectly successfully.
As many previous posters have ruefully observed - your life will irrevocably change once children arrive. You will certainly have to make significant and major adustments, but children can take part (or be lugged along) on quite a lot of your old activities if the activities are suitably adjusted in duration / content. They will gradually form their own preferences and you will have to continue to adjust what you do to maintain a parity of your, and their, activities. We're now at the begining of the teenage years so another new phase is begining...