My parents generally had a "do it when asked" approach so we never had chores we had to do without being asked. At some point they pointed out this gave all of us more flexibility in case we had a lot of homework a given day or something. I conceded that this trumped predictability. They were probably just not organized enough to keep track ;) The three of us turned out fine (middle sister is kind of messy...but she does know how to clean).
When I was 6 or 7 I would wash dishes quite gladly upon request (not all the time, and generally easy ones--no pots and pans or dried on cheese), I'd make my parents coffee in the drip maker on weekend mornings, and clean my and my sister's room after sufficient fighting with my mom. (Side note: I've since read that kids at that age may have trouble with breaking down huge projects like "clean your supremely cluttered room" into smaller steps or dealing with very fiddly storage systems. Fairly general bins are apparently easier for kids than boxes+shelves. This is secondhand knowledge, though.) I also remember baking a cake one time, and my mom tells me she started me helping in the kitchen when I was 2 or 3 (cutting eggs and boiled potatoes with a dull knife). So I probably helped with dinner some. I would watch my sister in the other room/just outside the apartment/while my mom ran to the laundry room (So 5-10 min chunks. Sister was 20-36 mos. This was the early 90s.)
Sometime around 8-10, I was loading and unloading the dishwasher, could clean the whole kitchen if sufficiently motivated (I remember doing this once and surprising my mom), clean the bathroom (with toilet bowl cleaner and windex+paper towels), vacuum. Again, all of this if/when asked and usually with complaints. I did like cooking (trying new recipes) though. I got up on my own and got myself ready for school. Mom would get up just before I left and see me off.
11-14, I started occasionally cooking/serving simple meals (pasta, boiled potatoes, eggs, hot dogs, cutting salads, etc) and eventually more complicated ones (stir fry, pancakes, soup); helping with, then doing laundry (it had to be taken to the apartment laundry room; my youngest sister started on this earlier because we had in-unit laundry). Oh, and at 11 I started middle school and made my own lunches (before that I got free school lunch).
By mid-high-school I was pretty self-sufficient, chores-wise (i.e. could do basically anything, though our family always did laundry jointly). Actually, 16 was when I learned to clean sink drains because dad had a torn meniscus and mom had back pain so neither could contort to get under the sinks which clogged every 6 months in that apartment (rented condo). WORST. CHORE. EVER. But by that point I could see how it had to be done...