TripJournal is hailed as the #1 Travel application by Google and is available for the iPhone/iTouch and Android devices. It allows you to document all of your travel experience and easily upload them to your friends, including full screen photos, videos, comments and blog entries. It is currently compatible with Facebook, Flicker, Picasa, YouTube, and Twitter. Read more here.
NYTimes.com apps allow you to access the latest news headlines, games, and features on many mobile devices. There are apps available for the iPad, iPhone, iTouch, Palm Pre, Android, and BlackBerry. See more at their apps page.
Alarm Clock PlusV2 This Android app requires you to solve a math problem to turn off the alarm. Other features include: unlimited alarms, 4 levels of math problems, the ability to turn snooze on and off, gentle alarm (increasing volume), and the ability to launch any app as an alarm. For instance, you could choose to wake up to the Pandora Radio app. Read and download here.
Wikipathia: The Wikipedia Path Game is a free app for iPhone/iTouch and Android devices. The goal is to connect from one article to another article using only the links on the pages, in the shortest possible steps. You are given two article titles (which you can change if they seem too easy or difficult) and a list of outgoing links for the first article. Read more about the iPhone app here and the Android app here.