The English version is currently under construction so many sections might be only in Czech.
You can find hiking/trekking maps of different countries here. The data are provided by the Openstreetmap project. Their main advantage is that they are legal to download and use for free (see the license). The main disadvantage is a possible incompleteness of the maps. The maps are created by the Openstreetmap contributors, if you find a mistake or a missing feature, you can correct it yourself.
The maps are generated mostly for the Czech audience, you might experience some Czech in map description or elsewhere - this is not a bug (I would have to re-generate the maps for a different language otherwise).
The maps are currently generated once per month, which is enough for most uses. If you wanted even more actual map, or to change how things are displayed, I'm providing the mkgmap style files. You can read how to generate maps on a Openstreetmap Wiki page.
Maps of the countries being currently generated (regularly generated in green, one-time generated in yellow):
You can find several similar projects on the Internet already. A nice trekking maps for Czechia and Slovakia can be found on the page of Dave Luv. The maps have their own original style obviously written from scratch and one can see the amount of work invested. However I don't like the rendering of hiking routes and on my Garmin eTrex 30 the maps are too slow.
Nice maps on which I based mine are Frikart.no. They don't have marked hiking trails and I changed most of the rendering, but I can recommend them for countries that I don't render (yet ;)).
Many hiking maps covering most of the world can be found on OSM-Garmin maps.
A customized hiking map of any area can be generated on Bbbike.org.
A nice list (in Czech) of where to download maps of different countries is on GpsFreeMaps.
A few screenshots from Garmin BaseCamp, style version 0.12: