I have a 4 yr old daughter and a 4m old son.
I don't really remember the moment when my daughter became a big kid so there is a blurred line between those categories for my list. She continues to play with the transition toys as well as some of the younger toys.
Baby- Sophie, soft books, ball (safe for chewing on, blanket (for tummy time,peekaboo and cuddling), big kid tooth brush for chewing on, spoon, chime garden, simple car to chew on and play with, piano/key board, Music cd's, a few cuddly toys (implore relatives to leave these choices to you or you will have a giant collection.), mirror, mesh basket for foods like apple pieces,
Toddler-board books, something to ride on, something to push, something to pull (wagon, dog on wheels, a backpack on wheels), silky scarves from thrift store (being cautious about strangulation), a box with a lid for putting things in, a box big enough to crawl into, one or two baby dolls, tunnel, something to pound on, shape sorter, stacking ring and cups, jack in the box, wagon to be pulled in, simple wooden puzzles, purse, toy phone, wallet, toy keys, drinking cup, a spiral tower that a ball rolls down,
Transition- kitchen set, table with chairs, baby cradle, baby stroller, "Hi Ho Cheerio", "The Lady Bug Game", "Memory", guess who, crayons, play dough, paint, a toy broom, drum, piano/keyboard, shakers, harmonica, kazoo, the mechanism from a wind-up music box, Blocks, 24 piece puzzles to play with mom and dad, view finder, bean bag for sport and pretend play, Journal to doodle in while mommy writes in her journal, play food, toy lap top (my baby boy Loves this too), tap shoes from a garage sale (use caution as these can be slippery), spinning top,
"Big Kid"- balance bike(we actually had a tricycle that she loved but I wish we had gotten a balance bike instead or as well), small mugs, plates and other great finds from the thrift store, books, craft making kits to play with an adult, "Go Fish" with regular playing cards (great for learning numbers), Play Mobile toys and figures, flash light, bag or purse, jewelry box with play jewelry, dress up clothes from the Halloween sales at "Once Upon a Child", A plant that she choose and takes care of, beads and string or pipe cleaners, a cooking apron for helping in the kitchen, a bicycle, a basket for her bicycle, cars, off brand Thomas train tracks and trains, a face watch, more complex puzzles, slinky, Plan Toys Balancing Cactus (2 of them makes this more fun and challenging), silk flowers for play kitchen and dress up games, wand and crown, kid scissors, mom's old digital camera, , easel,
Starting to be interested in- yo-yo, remote control car, Legos,