Opera Mini
Opera
Best mobile web browser.
Mobile webpage: mini.opera.com
Computer webpage: operamini.com

Gmail
Google
Email application for Gmail (in United Kingdom & Germany, it is 'Google Mail' instead of 'Gmail')
Mobile webpage: m.google.com/mail
Computer webpage: google.com/mobile/sony/mail

Google Maps
Google
An application which lets you view maps and satellite imagery.
Mobile webpage: m.google.com/maps
Computer webpage: google.com/mobile/sony/maps

Yahoo! Go
Yahoo!
An application providing Yahoo! services.
Mobile webpage: get.go.yahoo.com
Computer webpage: mobile.yahoo.com/go

Calc
Roar Lauritzsen
A simple scientific calculator (RPN) with many functions.
Mobile webpage: midp-calc.sf.net/calc.jad
Computer webpage: midp-calc.sourceforge.net
(It is strongly recommended to view the computer webpage first, in order to download the appropriate version of the application for your mobile. The mobile webpage consists of the general version.)

MiniExcel
Simprit
A spreadsheet application.
Mobile webpage: simprit.com
Computer webpage: simprit.com/miniexcel

Graph2Go
Math4Mobile
A special-purpose graphing calculator that operates for given sets of function expressions.
Mobile webpage: math4mobile.com/d/graph2go.jad
Computer webpage: math4mobile.com/applications/graph2go

Solve2Go
Math4Mobile
It supports solving equations and inequalities conjectures based on visual thinking.
Mobile webpage: math4mobile.com/d/solve2go.jad
Computer webpage: math4mobile.com/applications/solve2go

Quad2Go
Math4Mobile
It is a handy tool for learning about quadrilaterals.
Mobile webpage: math4mobile.com/d/quad2go.jad
Computer webpage: math4mobile.com/applications/quad2go

Sketch2Go
Math4Mobile
It is a qualitative graphing tool.
Mobile webpage: math4mobile.com/d/sketch2go.jad
Computer webpage: math4mobile.com/applications/sketch2go

Fit2Go
Math4Mobile
It is a linear and quadratic function graphing tool and curve fitter.
Mobile webpage: math4mobile.com/d/fit2go.jad
Computer webpage: math4mobile.com/applications/fit2go

KD Player
Knyzhov Dmitry
A customizable audio player with more features than the native Music Player or Walkman. For more info click here.
Mobile webpage: easter-eggs.net.ru/KDPlayer/EN_Versions.php
Computer webpage: easter-eggs.net.ru/KDPlayer/EN_Versions.php

The above applications are free, reliable and useful. There are many other mobile applications on the Internet, but most of them aren't reliable, useful or well-designed. Other mobile applications include 'Wayfinder Earth' & 'Wayfinder Active' available at wayfinder.com
Tip: Always download applications from their respective original websites, so your applications are true and up-to-date.