A few years ago when we were having a really hard time getting (and keeping) our 2 year old in bed, we began a tradition of making a list of routines and posting them. Now our 2 year old is 7 and we're still doing it, but we've added tasks

as she's gotten older. We've found that writing the routines down and making the list visible for the child is very helpful. The following is a list of the tasks we put on our routine list.
Keep your list of routine tasks relatively short. Too many tasks are overwhelming. The older your children are the more tasks you can add.
For
children 2-5 years old I posted about 5 tasks for morning and 5 for before bed.
Morning: eat breakfast, get dressed, put away pjs, brush teeth, do hair
Before Bed: put on pjs, brush teeth, go to the bathroom, get a drink, story time
For
children 5-7 years old I post about 10 tasks for morning and before bed.
Morning: make bed, put bed buddies on bed, get dressed, put away pjs, eat breakfast, brush teeth, put away toothbrush, do hair, feed dog, pack school bag, get outside clothes on (we live in Canada where it takes a good 5 minutes to put on ski pants, boots, mitts, hat, etc. in the winter)
Before Bed: pick tomorrow's clothes, put on pjs, put today's clothes away, brush teeth, put away toothbrush, go to the bathroom, stories
I haven't tried using a routine list for kids older than 7, but I would highly recomend it. I'd just keep adding tasks as I found it necessary.
I've also posted lists of chores.
For children 2-5: My four year old is able to empty the dishwasher. I ask her to put all of the dishes that belong below the counter away herself and the dishes that belong above the counter on the counter and I put those away. We do all of this while singing a song or two together. My four year old is also able to set the table (usually with a bit of help from me). Other chores include: tidy toys, dust, tidy books, feed the dog, match socks.
For children 5-7: All chores on the 2-5 year old list, sort laundry, fold their own laundry, put away their own clean laundry, take dog out to pee, make bed
With some of these chores I've had to simplify things. For example, bed making used to be very complicated with a top sheet, blanket, and bedspread. I simplified to just a blanket with a duvet cover. I keep an extra duvet and switch the duvet cover every week or so, as often as I would have washed the sheets previously.
What routine tasks and chores do your children do that are important in your family?