The short answer is VOR and direct navigation are both used often. GPS is becoming more popular and more affordable but there are still many general aviation aircraft not so equipped and many pilots not trained in its use. (Caution: flying GPS in Flight Sim DOES NOT train you to fly GPS in the real world). Even with GPS, many flights cannot be done direct because of intervening restricted or prohibited areas, and at low levels, other controlled airspace.
I don't fly with GPS but as an example, if I had GPS in my aircraft and wanted to fly from here (Mesquite, NV) to Reno direct, at most times I could not do so because I would have to fly through the Nellis military restricted areas and they are usually hot and unavailable for civilian traffic. So, when I fly to Reno, I have to make wide detours to avoid the restricted areas and would have to do so even if I had GPS.
JTH: An airway is usually longer than the defined path between two VORs and each airway is named. The low level airways in the US always start with "Victor" or "V" on the chart and ends with a number. A defined airway may be cosiderably longer than the distance between two VORs. For instance, an airway may begin at one VOR, run to a second then a third then a fourth, and terminate a fifth or more. Just one example, V27 runs all the way from San Diego to Seattle and is defined by at least a dozen VORs. The course between VORs on each segment may not be the same between one VOR and the next and, in fact, courses can an do change in the middle of a segment at an intersection.
In VFR flight, many, maybe, most flights are done off the airways. As long as you do not penetrate controlled, restricted, or prohibited airspace, you can fly anywhere you want to in the US without even talking to ATC. For those kinds of flights, VOR's are often used for navigation.