I am not aware of any country that has direct database access for free (apart from Norway). So if you find any - I would also be VERY much interested :)
M K Horn and colleagues published several compilations of global oil and gas field data, including a burial history database consisting of data compiled from the literature (presumably by graduate students or interns). To organize these >850 BHCs, it was necessary to create a map of the relevant basins and fields. The maps associated with the Giant Fields papers (AAPG publications) often only locate fields by points, not polygons. At UT, we had the data on a CD-ROM, but portions of it (and the subsequent publications) are scattered around the internet:
AAPG has a map of the basins and points at http://gisudril.aapg.org/Website/bhist03/viewer.htm . I believe it is possible to download the digital data.
AAPG has more available in their datapages, e.g.: http://www.datapages.com/gis-map-publishing-program/subscription-content-databases-atlases
AAPG Memoir 78 included a CD-Rom with tabulations for the Giant Fields, some detail available here: http://www.searchanddiscovery.com/documents/2004/horn/index.htm . The Giant Fields database was updated through at least 2010, but I haven't found the digital data online yet. Catalog entry for one of the Giant Fields CD-ROMs: http://www.worldcat.org/title/giant-oil-and-gas-fields-1868-2005/oclc/61850432
Australia Geoscience has a petroleum wells database (though its a bit tricky to aggregate the data): http://dbforms.ga.gov.au/www/npm.well.search
For the US offshore, the BOEM website has GIS data, though it will take some combining of regional datasets: http://www.boem.gov/Maps-and-GIS-Data/
The publisher Springer has published a very extensive (and I believe expensive) field by field data base by Colin Campbell. To my knowledge it is fairly thorough. Jean Laherrere of ASPO France also has a very thorough data base but I do not think it is published explicitly.
It would be a very good project for someone knowledgeable to integrate all of the good information given in response to this request. We need a good world summary, with uncertainties. The paper by Hallock et al (2014) gives a good argument as to how lower estimates of EUR (ultimate extractable resources) usually are the better ones:
Hallock Jr., John L., Wei Wu, Charles A.S. Hall, Michael Jefferson. 2014. Forecasting
the limits to the availability and diversity of global conventional oil supply: