The correct answer is that you can OWN any damn airplane you want. If I was wealthy enough, I could buy a B-2 stealth bomber and put in my back yard. Bill Gates has a sleek F-5 Tiger in his flight hangar. Paul Allen owns a Mig-29. And yes...people do own more modern warbirds such as the F-15 and F-16.
But there are of course conditions and stipulations. You cannot OPERATE a privately owned aircraft above the speed of sound unless you are in international waters. You cannot carry or FIRE live ordinance either. But you CAN own a military airplane that has some, if not all...of its sensor and targeting equipment installed. Again....with more conditions and stipulations.
**Edit: OK I just spoke to a representative of the Historic Flight Foundation that restored and privately flies a Mig-29, and a person at Seattle Flight Standards District Office. Here are the facts, so you can go right ahead and give these folks the bird if you're feeling adolescently rebellious:
1. Age of aircraft and country of registry is irrelevant. That means that it is just as legal for a civilian to purchase an F-22 Raptor directly from Lockheed as it is to buy an old L-39 Albatross from some Eastern bloc surplus dealer. Of course, the aircraft must be re-certified as Experimental.
2. A civilian operator cannot fly the machine above Mach 1.0 unless he or she is in international waters. (12 miles or more off the coast.)
3. Whatever weapons systems might be installed in the aircraft are removed if required BY THAT COUNTRY'S EXPORT LAWS. Naturally, most countries don't want to let a modern airplane with high tech targeting and fire control radar fall into the wrong foreign hands. But it isn't necessarily a requirement that we must remove them once we import them. Case in point: A Mikoyan Mig-29 uses a long range, look-down shoot-down radar. A General Dynamics F-16 (American fighter) uses LANTIRN/LITENING infrared targeting and terrain following radar. Guess what? If a bunch of wealthy collectors want to take their aircraft out 60 miles offshore one Sunday afternoon and practice "radar lock" on each other...that is perfectly legal. Try it on a civil registered aircraft anywhere close to U.S. airspace, however, and you're toast.
FAA Seattle FSDO: (425) 227-2813
Historic Flight Foundation, KPAE: (425) 348-3200