A list of 79 iPad apps I use frequently for personal productivity, media creation and sharing is available on this List.ly list. (December 2014)
An updated listing of our family's past iPhone / iPod Touch applications are listed on www.appolicious.com/users/wfryer. (Thanks to Lucy Gray for recommending Appolicious!)
A linked list of recommended iOS apps for iPhone, iPad, and iPod Touch is available on wiki.wesfryer.com/workshops/handouts/ios. (Updated 23 Dec 2010)
Our family's current installed iPhone applications (178 of them) are as of 01-24-2010: (Larger versions of these iTunes screenshots are available too: part 1 - part 2 - part 3 - part 4)
See the post "Holiday iPhone and iPod Touch Application Pruning" for clickable links of these graphics to larger versions which are easier to read, updated as of 28 Dec 2009.
Our family owns the following iPod games (mainly my daughters play them on their clickwheel iPods)
The following are iPhone web apps I either have installed and use currently, or have tried and like: