eCalc Scientific Calculator
While a calculator widget is part of the default Dashboard package, its functionality may be too limited for some. The default Dashboard calculator, which bears a striking resemblance to the calculator that was bundled on the original iPhone, contains functionality included on most basic calculators: addition, subtraction, memory buttons, etc.
For those that desire more in a calculator, however, there's eCalc's Scientific Calculator. This calculator provides niceties found on most scientific calculators, including sin, cos, tan, log and a host of other goodies. eCalc's Scientific Calculator adds some flexibility to its equation solving brawn. Much like how you can correct a particular letter within a word in a text document, you can edit a particular number or operator without changing the rest of the string. There are two versions of eCalc's scientific calculator. The trial/free version operates the same as the paid-for one ($14.99), except that it occasionally brings up a dialog asking if you want to purchase the full version before providing you with the solution to your problem.
Periodic Table by Travancore Analytics
Dmitri Mendeleev was a Russian chemist who created the first version of the periodic table of elements. Mendeleev's table has since been refined and extended in its layout, and serves as a fundamental backbone in the sciences.
Travancore Analytics has created a fairly useful Dashboard widget that provides a variety of details about each element. They include their grouping, periods, boiling point, melting point and a host of other information. This easily accessible widget serves as a pretty useful tool for quick on-the-spot lookups.
Google Translate Widget
For some, making sense of the periodic table is akin to learning a new language. While using Google Translate won't necessarily help you learn a new language, it can help provide you with a baseline understanding, or at least a sense of context, of foreign text. The Translate widget, created by Jeroen Wielandt, serves as a simple-to-use front-end for Google Translate. The widget also allows you to arrange your language(s) of preference in whichever order you desire.
Lastly, there's Sean Billig's Wikipedia Widget. This relatively straightforward widget allows you to view and edit complete Wikipedia articles in Dashboard. In addition, the widget supports Wikipedia account login and the ability to search in a particular language. For example, if you wanted to search for "Steve Jobs" in the French version of Wikipedia, you'd prepend "fr:" to the search: this search would look like "fr: Steve Jobs."
Readers, tell us about some of the widgets that you've downloaded, or created, that you find useful for learning.