The following SPARQL-applications would be extremely cool to have (and might deserve web interfaces to address regular historians and normal people).
Visualise corresondences on maps
The input is a time segment and a selection of names to explore, or a specified research interest. (Property:P97 is designed for such searches.
One would like to see who is writing to whom from where to where. Stanford created the first of these visualisations in the Republic of letters project and Nodegoat is loved by historians for the service: https://www.youtube.com/watch?v=eLDRNiJrRUc
You can set a time segment (like 10 years) and shift that window through time (like from 1500 to 1900) to see how certain correspondences developed centres and to understand the flow of information. We did not even find out how to draw lines between correspondents (let alone how to visualise developments).
Create StemmataProperty:P233 names the object - a book edition, a manuscript or any other thing that is genetically earlier. Property:P234 comes as the qualifier and offers a statement on what basis the object can be seen as a precedent. You might for instance link a translation to the edition that gave the original text.
The organisation is top down chronological (the guide lines in the picture above are not that beautiful, but dates on y-axis would be cool).
Objects can have multiple connections to earlier Items (a medieval scribe could use two books to create a new version of the text).
It would be cool if the P234 information became available - maybe on mouseover or through different colours to state how things are connected (like just a copy, a translation, an abridgment).
Visualise overlapping organisations
The Illuminati infiltrated Germany's landscape of masonic lodges. The Order lasted for about 10 years, but the members lived on in various organisations: lodges, student fraternities etc.
We have about 3000 of late 18th century people stated with affiliations Property:P91. It would be interesting to see which organisations shared members and which excluded each other - and it would be interesting to see how these configurations changed over time.
One think of Venn diagrams, overlapping circles of different sizes reflecting the respective numbers of members.
Visualise genealogical information
We have an increasing pool of genealogical information as in the case o Gotha's pastors - mapped over 500 years we can see how the pastorate was a business of families - we have not yet found out how display such information.