Is "General Aviation" a well-defined term in the US, in the EU and/or elsewhere?
The FAA does not include a definition of General Aviation in CFR 14 (aka Federal Aviation Regulations) Part 1 (General Definitions and Abbreviations), but, from a functional perspective, in the US, GA is generally used to refer to any civilian operations falling outside of Part 121 and some Part 135 operations (Commuter and Charter Operations - regional feeders have and may still operate under this section if they can meet the requirements, as it is more relaxed and easy to comply with than part 121).

With respect to the FARs, it's important to remember that Part 91 covers ALL types of flight operations UNLESS its provisions are EXPLICITLY overriden by another paragraph (as would be the case with an air carrier's Operating Specifications, part 121, 135, and other sections dealing with more specialized aerial applications). Part 119 also deals, in a very general sense with conducting flight operations for compensation. 

IMO, you're not likely to go wrong using the term to refer to everything civilian outside of scheduled carrier and medium/large cargo operations (e.g. Atlas, Evergreen, FedEx, UPS). The caveat is, of course, that GA operations are so diverse that this is more of an "everything else" category rather than the much clearer images conjured up by a flag/commutter/regional carrier or a large cargo operator. If you're unclear about whether a specific application or air operator falls under GA, go ahead and ask.  

The FAA division of airports is more likely meant to reflect that certain airports have certain primary intended purposes (e.g. many of the nation's largest airports do not allow Part 91 operations, only air carriers) and may require certain types of infrastructure in order to allow them to perform those roles.

And yes, using a 737 as a personal plane under Part 91 would fall under GA - Boeing even makes a specialized version just for that, see the BBJ.