For some time, one of our favorite activities around here has been what we variously call "the button game," "the bean game," "the jingle bell game," or "the rhinestone game," depending on what assortment of small objects we're using.
It's not really a game, in any literal sense of the word: It's a simple, and deeply satisfying, fill-and-dump extravaganza for toddlers. (For common-sense reasons, your kid has to be past the point of putting everything in her mouth.)
Get a big plastic bin, and add an array of dried beans or craft buttons or little bells or anything of that sort. Supply a selection of spoons, cups, funnels, cardboard tubes, pie pans -- anything a small child can use to scoop, measure, transfer, or pour.
The pleasures here are tactile, but also aural: I like to provide metal scoops, cups, and pans to heighten the delightful plinking sounds. When you've got a colorful array of objects to play with, it's visually exciting, too.
My kids can be engrossed for as long as two solid hours with this game. They love the feeling of mastery it gives them over a little manipulatable world. It's alternately contemplative (pick up little beans one by one) and rowdy (dump a whole pile of them on the floor ... whoops).
Once I made the mistake of trying to be all directive and teachy with this game: I brought out different colored cups and coaxed the kids into sorting buttons out by color. They grimly complied for a short while, then wisely ignored my directions altogether in favor of something far more interesting. By the end of that play session, they had created little button families, sent some of the buttons on long trucking expeditions, and made a really awesome button slide out of their vintage Fisher-Price parking garage.
Be prepared for mess: Even when they're truly trying not to spill beans or rhinestones or buttons all over the floor, it happens. If you're in a Montessori mood, you can bring out a whisk broom and dustpan and turn clean-up into its own game.