If I buy a military-style rifle in .308, can I safely fire NATO 7.62 X 51 in it?
If you mean a commercial firearm of recent manufacture, then yes, as a rule.
What about the converse?
It isnt recommended, as a rule.
It has to do with pressures in the chamber and varying headspace and throat dimensions.
Typical pressures for the two rounds are like this (approximate):
.308 WCF: 60,000+ cup's (about 62,000 +/-)
7.62x51 NATO 50,000+ cup's (about 53,000 +/-)
As a round destined for use by mulit-national forces, there can be no absolute guarantee that each and every make of firearm designed for the cartridge will adhere to the same stringent parameters. In fact, military rifles in general are known to vary widely in the critical dimensions mentioned, to allow for just what we are talking about - variances in both ammo and weapon tolerances.
Thus it was widely decided to maintain lower pressures in the NATO round than one finds in commercial grade hunting ammo.
If you want a comparable round, say for reference or reloading, look to the .300 Savage - the progenitor of the original .30 caliber "T" cartridge.
Too, while many older military rifles like the Spanish Mausers and some of the Enfields have been converted to 7.62 NATO, it is widely accepted that they are not of sufficient strength in either material or lock up to methods to accept the .308 in it's full house form, as already mentioned.
To read about it in detail, here's alink:
http://www.surplusrifle.com/shooting2006/308vs762nato/index.asp
Are any rifles of general availability to U.S. civilians even chambered in 7.62 X 51?
Yes. Milsurp rifles in the caliber abound and, of course, commercial rifles chambered for .308 WCF will accomodate the NATO round.