Here is a partial list of the apps I have on my Touch right now. These seem to have some potential to support thinking and learning and useful play:
Math Dice (a fairly basic game with some potential to support student exploration in the classroom).
Cute Math looks like it has some potential for preschoolers.
MakeNum - seems OK, but I have only looked at the light version so far.
For basic fact flashcard apps I like the Brain Blaze series - not perfect, but better than most - especially the progress screens.
Another neat app is the Bell Curve. It's not a game but as a tool to understand the relationships associated with the bell curve it's cool.
Touch Physics is a fun physics related game - gravity, levers, etc.
Number Line challenges players to sort out a set of decimals, fractions and percents.
Codewords is an interesting challenge - another app I'd like to take into the classroom for a discovery learning lesson.
Parking lot is a good problem solving game.
Word Party is a good fun 'guess my word' game for a small group.
Catch a mouse is a fun problem solving game and may even have some potential for supporting a discussion on graph theory.
Lemonade is a classic app that can help students to begin to understand the potentials and complexities that develop when you can manipulate more than one variable - but I haven't had a chance to form any judgement on this version.
Finally,Zentomino and Tanzen are neat puzzle games that support spatial reasoning and development of geometry sense.
I don't have a favorite calculator - any suggestions?