There are at least 3 free solutions:
1. OCAD6 from OCAD. An early version of the popular software, it is provided as freeware by OCAD. It probably looks a bit dated, but was useful in its time and is still an option for beginners.
2. Open Orienteering. This is a new open source orienteering mapping project that looks very promising. It can open OCAD 7 and OCAD 8 files, and save to them. Whilst it is still very much in development, its usable.
3. O-scape is another open source orienteering mapping project. It provides an extension to the popular open source Inkscape vector graphics software. Brooner interviews the author here on Nopesort.