iPad Games for 4 Year Olds

My kids love Where's My Water? It's a Disney app and it's really good actually. It's a game but it's really all about problem solving. It can actually be kind of hard and I've been stumped a few times and had to work it out. My 5 y/o is good at it and my 3 y/o mostly just likes to play to see the crocodile, but he is getting the hang of it! A 4 y/o would probably like it and you may or may not have to help them, it just depends. My husband and I have also been caught playing this game when the kids aren't looking! :)

Forest Flyer
PBS Kids
Bubble Guppies
All of the iLearn games
Nighty Night
Musyc

"Word Wizard" is a fun one. It helps with spelling and letter recognition.
One of my 4 year old's favorite app is just called "Disneyland". It's free from Disney. It's a virtual tour of Disneyland and had a "hide and seek" element as there are links all over that lead you to anything as simple as information about the attractions to classic animated shorts to games. It keeps her entertained for a very long time. Not totally educational but something just for the sake of entertaining once in a while isn't a bad thing.
We have a bunch of Wiggles apps that are great.
There are a number of Dr Seuss apps that are fantastic.
I always found it easier to look up things my kids liked and look for the apps that way :)

To add to all the great recommendations for far:

Duck Duck Moose - we have all the apps from this developer.

Darren Murtha Design - my 5 yr old DD played with the Preschool Memory Match since she was 2.5, and she still use the Drawing Pad app constantly.

Loud Crow Interactive Inc. - PopOut! The Tale of Peter Rabbit and other apps are really cute. My only complaint is that the size of their apps tend to be huge.

BTW, I think Loud Crow and Darren Murtha might be having a sale. I bought all my Dr. Seuss apps from Oceanhouse Media when they are on sale around March 2nd to celebrate Dr. Seuss's birthday.

Toca boca games are truly awesome!

I'm not sure how her grasp on letters is, but my 3 yo DD has 3 games in particular that she likes...

Endless ABC is a great one. It has 2-3 words for each letter of the alphabet. When she chooses a word, it comes up and a crowd of letters run through and scramble the words all over; leaving the outlines behind. The child has to put the letters back in place. While a letter is selected, it makes the sound of at letter. When the word is finished, it has a small cartoon explaining what the word means. My DD has been playing it for over a year now, and still loves it. :)

Lola's Party is a good one too. I only have the free lite version, but it helps. Actually, my DD started reading small words completely on her own a couple weeks after starting that one. :)

Leo's Pad is both of our absolute favorites. Each 'webisode' is $2.99, but very worth it (and i never pay for apps. lol.) So far there are only four. Each webisode is set as a storyline, where the child has to help Leo and his friends. It remembers your child's progress, and will get harder or easier based on their performance.

Angry Birds
Where's my Water
Cut the Rope
Reading Rainbow
Dr Suess's Band

Starfall and Snail Bob are 2 that I love!