What GIS (Geographic Information System) software is available?
Solution 1:
I use Quantum GIS, it is an excellent promising GIS package, has a very nice graphic user interface based on Qt, it can act as an interface to the venerable GRASS GIS tools too.
SAGA GIS which looks like a good second to Quantum GIS is available in the repositories. Do not forget Google Earth, even though it is not open source and have some limitations compared to a specialized GIS package it can be a very useful tool for some of your GIS work.
A useful set of command line tools to use for mapping and some GIS work are the Generic Mapping Tools GMT. The Geospatial Data Abstraction Library Utility programs are a must, you can get these by installing gdal-bin from the repositories.
Solution 2:
There are many GIS options available on Ubuntu. As you note, GRASS and Quantum GIS are two of the most widely used applications. They are probably the most user friendly options as well.
Thuban (install ) is another desktop option.
Mapserve is a web-based GIS option available in the repos.
The Ubuntu GIS team has a PPA providing the most up to date versions of geospacial related software for Ubuntu. This would be a good place to start investigating further options. The Debian DIS team is relevant as well.