Most of the people here just use graphics software, using only graphics methodology, and make up their own data from scratch, or just load up pictures of maps and then edit them as pictures. No special cartography software.

The GIMP and Inkscape are free, multiplatform graphics editors, the former for raster graphics, the latter for vector graphics, one of them, or both together should allow you to do pretty much everything that most people on this site are doing.

There are also some graphics tools specifically oriented toward fantasy map making. Campaign Cartographer, Autorealm, etc. These aren't true GIS tools as would be used to make maps in the real world. The fundamental problem is that they still treat the world they are mapping as flat. In general, they are specialized vector graphics editors.

Then there are a few tools that can deal with a round world, but are otherwise still graphics programs. G.Projector is an example of this and all it can really do is convert from one projection (Equidistant Cylindrical) to various other ones. I've written some software for drawing graticules for various projections (Those grids of latitude and longitude lines) that fits in this category too.

Then there is GIS, which is the software used to handle real geographic data. An all up GIS like ArcGIS or QuantumGIS is way overkill, though QuantumGIS is free if you want to try some overkill for yourself. These tools allow you to work with raw geographic data in the abstract. A full on GIS can not only load, convert, and edit, but can run complex analyses.

You can get free real world data from various sources, probably the most comprehensive is OpenStreetMap. I also get a lot of good data from Natural Resources Canada (aka, NRCan). A lot of that data will be in GIS formats like GeoTIFF, Shapefile, or GML though.