Native GIS software for Ubuntu (Linux)? The most famous is grass and qgis but it is not the only GIS software, is it?
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.
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.
There is a very nice overview of open source GIS applications that run on ubuntu on the OSGEO live dvd, and it is also available here: http://live.osgeo.org/en/overview/overview.html
This live dvd is based on ubuntu so all discussed applications can be installed on ubuntu, although some installation programs are better integrated (eg packages through synaptic).
You can try gvSIG:
You could also check out the stackexchange GIS beta site https://gis.stackexchange.com/, to see if there are Ubuntu or Linux users there with tips.
One of the thread answers includes the Ubuntu GIS ppa that andrew mentioned : "The awesome Ubuntu GIS repository makes it really easy to install and keep updated with open source GIS software. Anyone installing an open source GIS stack on Windows will appreciate this."
Link from the comment, for completeness : Ubuntu Wiki UbuntuGIS