Do real aircraft have something close to the GPS/NAV modes in FSX?
In the Boeing world, LNAV is Lateral Navigation, and VNAV is Vertical Navigation.

When LNAV is engaged, the autopilot will follow the Flight Management Computer (FMC) guidance laterally, i.e. left &amp; right.  When VNAV is engaged, the autopilot will follow the FMC guidance vertically, i.e. climbs &amp; descents.

LNAV is conceptually pretty simple: you have a magenta line on the map, your desired course, and the autopilot will follow it.  The points defining your course are database points in the FMC that may but certainly do not have to correspond with VOR's or other conventional NavAids.  You can use LNAV to fly VOR-to-VOR, or it can fly point-to-point-to-point equally easily.  (You don't have to tune any frequencies in either case.)

VNAV is a little more complicated, because you may only be cleared for some of what the FMC wants to do vertically.  Simple example: you're cruising at FL370, planning to start down at a given point so as to cross AAA at FL240, and then continue the descent to cross BBB and 10,000' and 250 knots.  ATC clears you to "descend at pilot discretion, maintain FL 290."  That means you can start down at whatever point you want, but until you get cleared lower later on, you can't descend all the way to FL240 or 10,000.  Yet.  Or maybe the controller needs to put you at FL350 right now to avoid a traffic conflict 100 miles ahead, and your clearance is "descend now and maintain FL350, pilot discretion FL290."

It's a lengthy section of Ground School how the pilot sets up the FMC and the mode control panel to accomplish all of this, but hopefully that illustrates some of the complexity of VNAV.

It's a good system; under typical conditions you can go into LNAV and VNAV shortly after takeoff and stay in them both until shortly before landing, and the FMC gives you smooth (mostly) and efficient guidance.