I have a 2000 Ram 1500 with the 360 that only has 80K miles and has basically been babied and maintained regularly. It seems to go through a quart of oil every 1200 miles, or so. I've never noticed any smoke, and no leaks.
Has anybody else experienced this? Any thoughts on what the problem is? Very disappointing...

Most likely culprit is the gasket for the intake panel. Seals the cover panel on the inside/bottom of the intake. Intake needs to be pulled to repair. Engines usually have spark knock from the burning oil decreasing fuel octane.

Sounds logical,as that is common on those. The replacement lower gaskets, vary and are usually better quality than the originals. Remove intake manifold, flip it over on bench and lower pan is right there.

Go to Hughes website. And get their kit

the first thing I'd do is pin down if it is leaking it or burning it (sheet of something under the vehicle overnight plus run it in your driveway for a good period of time. it might be slow buring it off just not fast enough to smoke enough to see. You might read "breakin secrets" at www.mototuneusa.com Might be a doing a combo of both

I went thru this with the V6 Magnum in my '93 Dakota.

In researching my engine, I came across a site that mentioned if you look down into the intake with the throttle body held open (NOT running of course!) and see black/oil, you've got a leaking plenum gasket.

Its really not that hard to do, and the peace of mind is worth the cost. Oh, and in my case, MPG improved too.

Hughes has a nice ridged alum plenum pan package with everything need to replace the cheap tin plate mopar used. 100 bucks or so. well worth the price.

if the intake has ever been removed it is sure to be sucking oil at 80,000 miles.

already been said so I am saying it again.

Hughes plenum pan package even if you have a shop/mechanic do the labor use the package from Hughes.

Thanks all! Looks like there's almost a consensus here.
I will try to peer down past the throttle blades and see if there's oil in the bottom of the plenum. Hughes kit is $$$ ($125+ now), but if it's a sure fix, I'll pay it.