I taught preschool for several years (2.5-4 yo kids) - and I did NOT do worksheets with my kids. I am a big believer in learning thru play and in incidental learning (learning stuff thru every day exposure).
I did LOTS of arts and crafts. I incorporated learning into my art and games. I'd pick a theme for the week - like caterpillars and butterflies. ANd we would do stuff in that theme like: reading books about caterpillars (Very hungry Caterpillar by ERic Carle), fingerplays about caterpillars and butterflies, making butterfly finger puppets and flying around the room, using playsilks and classical music to butterfly dance/fly, learning symmetry with butterfly print (cut out the paper, paint on one side, fold and press), caterpillar numbers (different colors circles each number 1-5 that kids glued together and then added as many legs, etc as they liked wherever they chose), egg cartons cut into various sized catepillars that we painted and decorated (and counted the "bumps" on). I also made a huge posterboard of the Very Hungry Caterpillar book with a caterpillar and butterfly cutouts and made holes in all the foods - so the kids could use the posterboard and cutouts to retell the story. It had great opportunities for incident learning about foods, colors, numbers, and science. I also got a bug box so we could watch the caterpillars grow, change into butterflies, and then release then in the playground.
So they were learning - but they were learning language, math, science, social, motor - all while they created stuff and played.
DS - he is a little over 2. I provide him with only open ended play stuff. He has blocks, puppets, kitchen stuff, trucks, baby dolls, art supplies, etc. I limit the electronic stuff (we have almost none - even gifts get donated). I also limit what TV he watches. I did not want him to have any TV - it has been proven to delay language development in young children, it can lead to desensitization to violence and snarky behavior, and it can lead to children not getting enough exercise. DH started letting DS watch TV on weekends while I worked - so I made a rule, one hour in the am and pm, and only approved shows - which in our house is Sesame St, Barney, and Blues Clues. I like the educational content of these shows - on all levels not just ABCs and 123s, but the social/emotional development content. Due to my pickiness, we have tons of appropriate DVDs. Usually, DS has a video on, but is busy playing blocks or reading - he listens to it while he plays other stuff.
He also has a TON of books. Almost a whole bookshelf full. Reading is very important to me. I started reading to DS in utero, and began reading to him in arms while still in the hospital. DS LOVES books. We go to the mall, he will bypass the toystore and drag us to the bookstore, begging for more books.
it makes me really proud. Again, no character books. Just really good books. We have animal books, ABC books, number books, etc. A little bit of everything. he picks out whatever he feels like reading, whenever he wants - which is quite often.
Anytime he shows an interest in something - I try to provide him more of that subject. I feel like I'd be holding him back if I didn't give him more play materials on a subject he enjoyed and was really interested in. I remember feeling really bored and stifled as early as 2nd grade - and I never want that for him. I don't teach him - just provide learning opportunities for him to do as he will with.
He has been obsessed with ABCs and number books and toys for about 6-8 months now. So we keep buying him more books, puzzles, fridge magnets, etc. I do not quiz him, give him worksheets, or anything like that. But before he turned 2 - he could recognize all his letters when asked, and he named most of them as he read his books or played his magnets/puzzles. He also knows 1-10 (except 7) and loves to point out the numbers on store displays and registers. Now he discovered upper and lowercase, so he is obsessed with that. He will spend all day sitting with his magnadoodle ordering me to draw such and such letter - big and little versions of course.
Like I said before - it isn't about structure lessons or "teaching" - just providing him with learning opportunities as he shows interest. I personally feel like I would be doing him a disservice if I didn't provide him with opportunities and educational materials, but also a disservice if I sat him down with worksheets or flashcards.