My daughter was one on December 1st last year - she got a smart trike, a sand pit, a water table, a rocking horse, lots of board books, musical instruments, a leapfrog activity table, wooden bricks, a little pop up tent and play tunnel, the tomy squeaky eggs, elefun ball popper, happyland castle (she just liked the figures when she got it but started playing properly with it later in the year), the vtech picnic basket, the fisher price laugh and learn chair (she has played with it EVERY DAY since), fisher price hand bag, fisher price teapot, a bubble machine from ELC, Melissa and Doug wooden puzzles...
That's all from birthday AND Christmas from us and everyone else too, but hopefully it gives you a few ideas xx