Wine is a free compatibility layer that allows some Windows programs to be used under Linux and other Unices. It is not perfect, but may work out of the box for some of those applications you need. As was revealed in the 2007 Desktop Linux survey at DesktopLinux.com, the majority of Linux users who run Windows programs on Linux use Wine. However, seeing as the default interface is primarily a CLI, it can be confusing to use to new Ubuntu users to use. Here we will simply install Wine and install K-Meleon 1.1 as an example.
Your first and easiest option is simply to install wine from the Ubuntu universe repositories. If you have not already, there are instructions for enabling the universe repository with Synaptic here.