We never paid for chores either - you help out and that has always been expected.
Our kids are not really shoppers - but we're not either, so some of that you may be able to avoid by your shopping habits. I have friends who shop, so their kids shop. For instance, they go to the mall a lot, or go to stores like Walmart or Target a lot, so their kids have ample opportunity to ask for things (toys, etc.) a lot. We don't take our kids to those places. If I had to go get things, I left kiddos home with Dad when I ran errands etc. It was just easier.
If you want your kiddos to learn the value of making money but still want them to help out at home and not to expect to be paid for it, you can do what we have done - which is extra chores/work for pay.
My kids this time of year raked leaves - helped put things away for fall/winter, helped with yard work (beyond what is just typical help). Anything I did not want to do, that I could assign to a child - I would say "Who wants this job for (a few dollars)" up to $10 for a bigger job.
The thing is, once your kids are old enough to mow the lawn, that's something I would pay for. Then they can charge neighbors for it. Ours did. Some kids actually make a fair amount doing jobs like that. So one of ours did yardwork/maintenance as part of his summer job this year - wasn't hired for it, but because he knew how to do it (doing it for us for years for these $5 odd jobs), he got picked to help out the boss, and was the chosen kid for many odd jobs at work this year.
You don't feel like doing that project you've been putting off? Pay two of your kids to help organize something for you - give them a couple of bucks each.
Things like loading dishwasher, setting table, etc. should be part of regular chores (in my opinion) but things that make your life easier ... pay them for. Why not? They need to learn these skills anyhow for when they are out on their own.
Has worked for us. Good luck :)