The holidays are coming and the big question is, what is your 1 (2, 3, etc) year olds favorite toys. As this question came up again my daughter was playing with a pair of rain boots. That brings me to our favorite "things", not necessarily "toys".
For the crawler, our favorite thing is anything they can pull up on, push, bang with their hands, empty, throw, etc. A full laundry basket is a good one. Ok, they like push toys and activity tables. But a full laundry basket (full of anything, not just laundry) is stable enough to support them pulling up but still able to be slowly pushed around (as oppose to some push toys that go so fast they fall down). When they're bored of that they throw everything out one by one. Soon they land on their bottom as the basket tips on its side from less weight. From there they empty the rest and move on to playing with the basket. Eventually it ends up upside down. Now the larger side is down so it's more stable and they pull up on it again. They can bang on the bottom like a giant drum and push it around some more. You just gained 15 minutes of independent play from something you already had in your house. It grows with the child too. Soon they become climbers that will get in and make it a nest, car, boat, rocket, house, etc.
Toddlers favorite toys are the dishes. You can buy plenty of toddler size kitchen toys. Or you can raid everything plastic you have. Soon your toddler is using your little pot and wooden spoon as a drum while wearing your colander as a hat. When that gets old they start using your plastic ware as stacking toys. The really fun mom even lets them take a plastic pitcher and some cups onto the porch or into the tub to practice pouring. If you want to get mommy if the year you can even let them "wash" them in the sink. If your not so brave, some large (in other words, not choking hazard size) Pom poms, balls of socks, old jar lids, or homemade bean bags can be put in and out of them. Bonus, this is a good time to practice colors, shapes and counting.
Preschoolers love being like big kids. Give them a coloring book and crayons and they will color for a bit. But give them a piece of paper and a pencil or pen and they'll "write" and do "homework" like the big kids for much longer. Do you want to step it up a notch, google a cooked playdoh recipe (cooked lasts longer and has a better consistency than the no cook recipe and homemade crumbles less than store bought plus uses so much salt they don't try to eat it after the first taste). The staples for any craft friendly pantry are flour, salt, cream of tartar, dawn dish soap, glycerin, white school glue, starch, rice, kool aid packets, and cornstarch, with these and a couple plastic containers your ready for any rainy day.
School aged kids can get by with bags and blankets. With the blankets they can make forts, tents, castles, puppet theaters, hammocks, etc indoors or out. With the bags they can pack flashlights, snacks, sticks, rocks, leaves, socks, etc for crafts, picnics, and play. Sticks become guns and swords (for both boys and girls whether you like it or not). They can also be crafted into wands, mobiles, etc. Rocks are good as hammers, weights, money, treasure, or painted as paperweights or pets. Socks become balls, treat sacks, beanbags, gloves (or animal "paws"), or puppets. Leaves can be pressed, printed, rubbed, used as tickets, money, for a collage, or hung from the stick mobiles.
All the older kids need is a library card and the imagination you have been nurturing with the above "toys" since they were born. A ball or box thrown into the mix for any age doesn't hurt either. Those too tight clothes you have figured out you'll never fit in again, the heels your afraid to walk in, and a pair of rain boots add the perfect "outfit" to their make believe play. You'd be surprised what you can do with a t shirt (smock, cape, mane, ninja mask, purse, etc).