This page lists free, in the monetary sense, tools, data and other resources for making maps. Although I’m concentrating on open source, open licensed materials, not everything given here meets that criteria. So check the individual licenses before use, and be aware that dependencies may not be open.
Bamboo DIRT: DIgital Research Tools catalogue, section for cartographic tools: http://dirt.projectbamboo.org/categories/mapping
FreeGIS: Dormant, but still useful, catalogue of FLOSS GIS tools. http://freegis.org/
Debian GIS: Packages for the Debian Gnu/Linux distribution. http://wiki.debian.org/DebianGis
Ubuntu GIS: Software for the popular linux distro Ubuntu and its many variants. https://wiki.ubuntu.com/UbuntuGIS
MapMe: Free to use online map annotator, with crowd-sourcing possibilities. http://mapme.com
Qgis Cloud: Free and paid-for map hosting using the best known open source mapping software. https://qgiscloud.com/
MapsData Online Converters: An array of online tools – free to use but not open source – for converting data into co-ordinates etc. http://www.mapsdata.co.uk/online-file-converter/
QGIS: The opensource alternative to the likes of ArcGis. http://www.qgis.org
MapWarper: for geo-correcting old maps, and lining them up with modern maps. http://mapwarper.net/
Story Map JS: “A free tool to help you tell stories on the web that highlight the locations of a series of events.” http://storymap.knightlab.com/
Temporal Mapping Tools
For combining time and space. And yes, most of these tools are called Timemap.
Neatline: Geotemporal exhibit-builder for the Omeka web-archives platform. http://neatline.org/
TimeMapper: From the good folk at the Open Knowledge Foundation, Timemapper “lets you create elegant and embeddable timemaps quickly and easily from a simple spreadsheet.” Requires a Twitter account and Google spreadsheets. http://timemapper.okfnlabs.org/ Introductory tutorial: http://okfnlabs.org/blog/2013/10/11/timemapper.html
Atlas of Historical County Boundaries: Shapefiles for the United States. Licensed under CC-BY-NC-SA. http://publications.newberry.org/ahcbp/index.html
Open Street Map: Crowd-sourced map of the world, under a free license, with a veritable ecosystem of tools and projects based upon it. http://www.openstreetmap.org
Amsterdam Open Geo Data: Amsterdam Open Geo Data
Antique Maps of Iceland: Some 770 maps, all available for download. http://islandskort.is/en/
ICGC Cartoteca Digital: Large collection of well digitised maps from a Catalonian collection, but sadly licensed under a no derivatives CC license. Downloading seems to require logging in. http://cartotecadigital.icc.cat/cdm/
LSE Charles Booth Poverty Maps: Available in high quality reproductions from Flickr.
National Library of Scotland: Many maps, mainly of Scotland and the rest of the British Isles, including early Ordnance Survey maps. http://maps.nls.uk/index.html
Peliagos Project: Medieval maps, atlases, charts and itineries, hosted by the British Library. https://data.bl.uk/pelagios/
Perry-Castañeda Library Map Collection: Many maps, albeit of varying quality. http://www.lib.utexas.edu/maps/historical/
Rumsey Collection: Very large, and generally very well digitized, collection of maps spanning the whole planet. Many maps downloadable and in public domain or Creative-Commons-licensed; but no way I can see of downloading geo-referenced ‘warped’ maps. http://www.davidrumsey.com/
Wikimedia Commons: Many freely licensed maps. http://commons.wikimedia.org/wiki/Category:Maps Note
Map Icons Collection: Fantastic collection of CC-BY-SA licensed icons. http://mapicons.nicolasmollet.com/
Maki: More map icons, this set from Mapbox: https://www.mapbox.com/maki/
Last updated 5th June 2017. This list is public domain, and may be freely adapted for any purpose whatsoever.