Internally, our data is mostly stored in TAB format and analyzed within MIPro (v16 with a bit of v15). In addition to that, we use SQL Server for storing databases that we use for address fixing (such as fixing city and street names) which is done by our own internal program that uses both synonyms and an algorithm that finds closest matches. We also use some .NET applications that do things such as converting coordinates (we convert Israeli coordinates, ITM, to LatLon and back).
As for our clients, in addition to the ways we store, many of the large corporations using Oracle in their legacy programs and some moving towards PostGIS now, especially newer departments that deal with big data.