I have a 4yr and 2yr old girls, so I have read other comments with interest. Will definitely be trying some of those out. I've only used Amazing Alex and agree its a great puzzle for my 4yr old.
Here are some of my own suggestions.
Motion Math Hungry Guppy - For very simple addition. You need to join together bubbles holding 1, 2 or 3 dots to make a new bubble matching the number stuck on the side of a cute orange fish, which then swims over and eats the matching bubble and gets bigger and bigger until end of round.
Happy Pig - Children's Logic Game - fill in missing items in a pattern arrangement - my 4yr old knocked this over in a couple of days but I am happy it served its purpose in that time. It was interesting to see her cognition go from incomprehension to mastery in that short time. Revisits occasionally.
Pit Droids - A generator spawns different coloured droids in one direction, and matching coloured arrows need to placed on the ground in front of them to turn them towards matching coloured pits. I've enjoyed helping her get started and now she can now do some levels herself. Got it after reading this review http://apps4ikids.com/2012/06/star-wars-pit-droids-surprisingly-educational-puzzler/ which discusses it being a preliminary training for programming.
Chess Pro With Coach by Christophe Theron - training for strategic thinking - not that my 4yr old is anywhere near that! but the computer can be set really dumb and slowly turned up over the next few years. It graphically suggests good moves and pieces under threat.
Timmy's Preschool Adventure - Simple pattern/puzzle solving. Animation is a little B grade but still engaging for both 2yr and 4yr old.
Kid Klok - shows numbers around the circumference for both hours and minutes - each a separate colour matching hour/minute hands and digital clock reading.
Flow Free - path planning - 4yr old picked it up much faster than I thought she would.
Team Umizoomi - numbers and simple math in an engaging presentation for both the 2yr and 4yr old
Bugs and Buttons - lots of cognitive mini-games - 2yr and 4yr both love it.
ToonTastic - just to round out with a non-science app - yet the decision making learnt from creative play is an important skill. Drag cartoon characters onto a background then record an animation with voice-over by the kids.