Some of the favorites of the kids I nanny for and at the Center where I worked enjoyed the books by Mo Williems and Doreen Cronin. I admit I'm not sure who enjoyed the books more--myself or the kids! Doreen Cronin's Clik Clak Moo is hilarious (so Duck For President) and I adore the Pigeon books by Williems.
My all time favorite is Snow Queen by Hans Ch. Andersen but I don't really think it's appropriate for a 3-year old. Maybe when she'll be around 7 she'll be able to apreciate it.
Oh ... I have a good post about this at my book blog if you want to check it out. Here is the link. It was part of a quiz I did but I picked books that I loved. For your daughter, "The Monster At The End of This Book" would be great. As would "The Very Hungry Caterpillar." My son also loved "Cloudy With A Chance of Meatballs" -- a little older but fun. And the Beatrix Potter books are great too.
I would highly recomend Out of the Nursery by Elizabeth Gauthier my son loves it and he is also 3. I also enjoy reading it to him and I love that it was printed in the USA. I found it on Amazon.com I have put the link below
I purchased Out of the Nursery the other day, thank you it is great. I also bought the monster at the end of this book, and green eggs and ham to add to the collection
The first book I learned to read was "All By Myself" by Mercer Mayer. I still love all the Little Critter books. I also loved The Little Engine Who Could. Really, that is one of my favorite books as an adult too. Nothing but believing in yourself even when other people doubt you. LOVE IT!