What OPNLguy stated is correct; but, whenever possible. most pilots prefer to get direct routings - it saves time and fuel. With the advent of long range nav systems it is the norm, at least here in the U.S. and Canada to get direct clearances nearly everywhere.
Here's how it's typically done. We will file a latitude/longitude fix which correspondes directly to the airport; or to a fix on a STAR; or to a an appropriate arrival gate for where ever it is that we happen to be going. For example, I am based in Oregon and we frequently fly to Teterboro, NJ. We simply file "lat/long direct" to the Wilkes Barre VOR (LVZ) then via the Wilkes Barre 3 arrival to TEB. We get that routing every time. The key is that we typically operate above FL370 eastbound, usually FL410 or FL 450 and FL390 or FL430 westbound. ATC is very accommodating when it comes to direct routings when you're operating at FL370 or higher. Going eastbound, on a leg of any distance, our altitude of choice would be FL410 initially, then FL450 after a couple of hours or so. At those altitudes, you seldom have to talk to anyone except, of course, for handoffs. (We've had these higher flight levels pretty much to ourselves until fairly recently, but now we're starting to see more and more air carriers up there.) There are still quite a few airliners that do not have RNAV equipment. Those aircraft are forced to fly the airways, unless of course ATC is willing to offer them vectors - which they often do. Most air carrier aircraft spend the majority of their time below FL370. This is still the most crowded airspace and, even with RNAV capability, direct routings below FL370 often involve a lot of vectors.
In the US, as long as you can get to FL370 or higher or stay below FL240 you can pretty much file direct to any two points. There are some caveats though. You've got to avoid active restricted areas and MOAs and there are areas where you will be given specific routings to specific arrival and/or departure gates and/or SIDs and/or STARS. In our operation we routinely fly coast to coast and border to border on a weekly basis. We are on direct routes 90% to 95%. In the mid and western US, it's common for direct airport to airport clearances. On either coast or from any of the major cities you usually won't be given a "direct to" clearance until you've passed one of those fixes or climbed to FL370 or above. Then it's back to business as usual.
Departures from the east coast corridor airports westbound are slightly more involved, but not really. You will still get all of the typically convoluted routings, but once you get above FL370 they will normally reclear you direct to destination. It's just a matter of keeping the climb up. As far as altitudes go, westbound we typically file for FL390 and climb to FL430 as soon as we are able.