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Found this [collection of links with some archaeological datasets][1]. It's just for UK though. 

Here's a teaser

    ARCHAEOLOGICAL DATA
    Source – BAA, Oxford Archaeology and Wessex Archaeology.
    Data – Archaeological data for Stansted and Heathrow Airports. Excavations by Framework Archaeology 1998 to 2004
    Format – Various, including ESRI format.
    Licence – Creative Commons Attribution-NonCommercial 2.0 License (see website).
    Cost – Free.
    Comments –
    Link - http://www.framearch.co.uk/stansted/index.html - Stansted Link - http://www.framearch.co.uk/t5/data-downloads/ - Heathrow T5


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Here are some [free archaeological datasets from the Swedish National Data Service][2]. 
![enter image description here][3]


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This one's from the [La Milpa, Belize][4].

![enter image description here][5]


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  [1]: http://wiki.osgeo.org/wiki/Public_Geodata_for_the_UK
  [2]: http://snd.gu.se/en/search-and-order-data/gis-data
  [3]: https://i.sstatic.net/4yeTG.jpg
  [4]: http://web.archive.org/web/20201105232038/http://www.bu.edu/lamilpa/
  [5]: https://i.sstatic.net/5HU55.gif
  [6]: http://lib.stanford.edu/gis-branner-library/gis-archaeology