I second the recommendations that others have given. My daughter is 21 months now but she still plays with most of these toys. She too loves the Parents Drum, all of the Leapfrog products especially the maracas, Fisher Price Sit and Spin Zebra, and the FP Laugh and Learn House. She actually received all of them as 1st birthday presents. She also likes the Fisher Price Amazing Animals Sing and Go Choo Choo. That one doesn't have much educational value other than learning the animals and their sounds, but it plays music and the animals all make a clicking sound when their limbs are moved that my daughter really enjoys! One more thing, I'd like to add books to the list. Around 1 year old my daughter really started to enjoy the books with different textures in them, usually different animals to feel. Right around 1 yr. old she learned to turn the pages herself and would actually sit with a book for 10 minutes or so. She still loves books and now is interested in pop-ups and ones with parts that move. In my opinion it's never to early to give a child a book. :)
My girls LOVE[D] the sit n spin zebra and also the fisher price laugh and learn chair. My older one is obviously too big for both now but when she was younger enjoyed both also!! My little one still plays with both and she is 20 months. I also recommend leap frog, wooden blocks, stacking cups (especially those made for the tub).