My company currently uses MapInfo Professional to map our client's addresses into territories. I have been asked to figure out a mechanism to do the same thing but real-time via a web service call. Is there any way to store the data from teh Mapnfo TAB files in a database and query it with lat/long in order to determine which "object" the lat/long belongs in? I've seen that there are multiple data formats for geospatial information, so if it isn't possible with the MapInfo TAB files, would it be possible with other formats? Am I coming at this issue in the correct way or is there alternative mechanisms for solving the problem?
If you have >= Version 10 of Mapinfo, it is able to read and write PostGIS natively.
PostGIS is a very good, open database for spatial data. Probably your best option is to convert your tab files to a PostGIS-compatible format and/or load them in.
You can then not only expose a service to test which territory an address is in over the web (you'll need some programming language glue) but you can also use any number of clients to view the data, including Mapinfo (and Mapserver, Geoserver, etc.). In this way your Mapinfo investment is protected, but you are free to experiment with other technologies that may be cheaper or more capable. Testing which polygon a point belongs to is pretty simple with the operators ST_Contains / ST_Within.
In theory, this is a perfectly feasible project, but the implementer will need to know a fair bit about databases, sql including spatial operators, and programming.
Stev_k is correct. MapInfo Pro does since v10 support a number of spatial databases, like PostgreSQL/PostGIS, SQL Server 2008 and Oracle. Oracle has actually been supported for at least a decade, so if that's your choice of database, older versions of MapInfo Pro will work as well.
You do not need to convert the dataset into a different format in order to upload it to the database - you can save it directly to the database thru File > Save as... in MapInfo Pro or you can use the free EasyLoader tool to upload it to your database of choice.
And do remember that for MapInfo to be able to work with spatial data in a database, you need to create a MapCatalog in this database - this can also easily be done using EasyLoader.