Most of this content was generated through the collaboration of participants in my session at THATcamp CHNM 2012.
ArcGIS - A really powerful mapping tool with all the bells and whistles. A lot of archaeologists use this because of how specific you can be with the location. However, it's not entry level. Most people I know who use it have taken training courses or have been heavily supervised while learning it. One option for training on the software is the Digital Humanities Summer Institute. Ohio State has a license for the software, and the Center for Mapping may have staff or faculty to assist you (this is merely a rumor I heard, so don't quote me!).
QGIS - An open source GIS application. I have no experience using this, but it seems to be a good alternative to ArcGIS.
Other mapping options:
ViewShare - Mapping tool that is relatively easy to use and especially useful if you want to connect images to the locations. One good example maps the locations listed on trade cards at the Brooklyn Public Library.
Google Earth - Probably one of the easiest tools to use. You can simply click to add markers, and you can add as much data to the markers as you want. One limitation to this is that there is no way to get the data out of it (ie you can't export a spreadsheet of all the coordinates for your markers). One way around that is to start with your data in a Google Fusion table and then convert it to a map. Fusion is still experimental, so there's no guarantee there in terms of longevity of your data or accessibility to the tool itself.
BatchGeo - Seems to work best if you have modern addresses for the things you are mapping. I don't, so I haven't attempted to use this tool.
Zotero Maps - Another resource I haven't tried out personally. For those of you who use, or are thinking about using, Zotero this might be a good, simple option.
History Pin - You can build a tour and mark each location with images. Not sure about how data is managed on this site, I haven't used it.
Georeferencer - Easy to use, web-based tool for georectifying historic maps. Simple export to Google Earth or GIS platforms. The David Rumsey Map Collection has tons of maps, and they can be slurped up by Georeferencer.
New York Public Library Map Warper - has a number of maps already georectified, but as far as I know only maps in their collection are hosted on the site. I used this a lot before I found Georeferencer.
General Resources for Education, Edification and FAQ:
Spatial Humanities Step by Step - Offers some instruction for specific applications and techniques. They probably have a few more tools described there that I have not posted here.
*note that all these great examples were collaborative efforts and received special funding or institutional support. In other words, these weren't made by independent graduate students as supplements to their dissertations!