I'm current military, Army, E-9...
There was some language in the last defense bill that changed the rules for off post housing. The Army did send out a mesage.
FY11 National Defense Authorization Act
SEC. 1042. PROHIBITION ON INFRINGING ON THE INDIVIDUAL RIGHT TO LAWFULLY ACQUIRE, POSSESS, OWN, CARRY, AND OTHERWISE USE PRIVATELY OWNED FIREARMS, AMMUNITION, AND OTHER WEAPONS.
(a) In General- Except as provided in subsection (c), the Secretary of Defense shall not prohibit, issue any requirement relating to, or collect or record any information relating to the otherwise lawful acquisition, possession, ownership, carrying, or other use of a privately-owned firearm, privately-owned ammunition, or another privately-owned weapon by a member of the Armed Forces or civilian employee of the Department of Defense on property that is not--
(1) a military installation; or
(2) any other property that is owned or operated by the Department of Defense.
(b) Existing Regulations and Records-
(1) REGULATIONS- Any regulation promulgated before the date of enactment of this Act that requires conduct prohibited by this section is null and void and shall have no force or effect.
(2) RECORDS- Not later than 90 days after the date of enactment of this Act, the Secretary of Defense shall destroy any record containing information described in subsection (a) that was collected before the date of enactment of this Act.
(c) Rule of Construction- Subsection (a) shall not be construed to limit the authority of the Secretary of Defense to--
(1) regulate the possession, carrying, or other use of a firearm, ammunition, or other weapon by a member of the Armed Forces or civilian employee of the Department of Defense while--
(A) engaged in official duties on behalf of the Department of Defense; or
(B) wearing the uniform of an Armed Force; or
(2) create or maintain records relating to an investigation, prosecution, or adjudication of an alleged violation of law (including regulations) not prohibited under subsection (a), including matters related to whether a member of the Armed Forces constitutes a threat to the member or others.
(d) Review- Not later than 180 days after the date of enactment of this Act, the Secretary of Defense shall--
(1) conduct a comprehensive review of the privately-owned weapons policy of the Department of Defense, including legal and policy issues regarding the regulation of privately-owned firearms off of a military installation, as recommended by the Department of Defense Independent Review Related to Fort Hood; and
(2) submit to the Committee on Armed Services of the Senate and the Committee on Armed Services of the House of Representatives a report regarding the findings of and recommendations relating to the review conducted under paragraph (1), including any recommendations for adjustments to the requirements under this section.
In a nutshell, the above forbids installation or unit commanders from requiring on-post registration of weapons owned by service members residing off-base. It applies to ALL branches of the military. It's not optional...it's a LAW...passed by Congress. 
Kimio:
At some point in your future, you may find yourself living off base (married or single, apartment or house). You may freely store any firearms you own in your off-base domicile without registering them with military authorities.
However, if you ever intend to transport a particular weapon back onto the base (say to utilize the base's recreational shooting range or hunting lands), you will have to register that weapon with the base law enforcement office or Provost Marshall. Bringing an unregistered weapon onto a federal installation is (IIRC) a federal felony. Such an incident occurring at the main gate (random vehicle search) will effectively end your career and put you in a world of hurt.
State issued CCW permits do not apply while on a federal installation...there is no CCW carry or vehicle storage of loaded/ready self defense weapons allowed. All firearms must be unloaded, stored in a locked case, and separated from their ammo while being transported on federal property. Additionally (and very importantly), your weapon must be accompanied by it's individual installation registration slip (just like you must keep a copy of your vehicle registration in your car). Once you depart/exit the base gate, local/state laws apply to you just as they do for any non-military resident of that state.
mehavy's post # 27 summed up ownership while assigned to CONUS basing nicely. It's not really that difficult a process, just inconvenient for younger troops living in community barracks or dorms. Having weapons in on-base housing (for married folks) is as easy as registering your weapon at the same office you register your vehicle and simply storing your weapons in your quarters. I've done it for years.
Another point to keep in mind is that you can purchase handguns in the state you are assigned to as a permanent party member. This means the unit you are assigned to (for a couple of years) after completion of basic/initial entry training. In other words, you do not have to possess a driver's license for the state the military transfers you to (or even be a legal resident of that state) in order to purchase a rifle, shotgun,
or handgun.
Assuming you are age 21 or older and meet standard purchasing requirements (no felonies, drugs, etc.), your presentation of an Active Duty ID Card, a drivers license from any state, and a copy of Permanent Change of Station (PCS) orders will suffice for constructive residency and purchase of handguns in the gun shops of almost any of the 50 states. There may be the odd exception (NY? HI?), but I've not yet encountered such. You may still have to meet state purchase requirements in certain onerous locales that require a FOID or "permit" to purchase or own. Fortunately, most states do not require them.
The cultural worm is beginning to turn with regard to on-post/on-base sales as well, with many military installations bringing back on-post sales shops (to include directly inside the Main Base Exchange). Weapons sold in an AAFES BX or PX are not subject to state or federal tax, which can be a bit of savings for a young Airman buying a new rifle, shotgun, or pistol. Good news for military members!
When I lived in the barracks, my experience with Privately Owned Weapons (POWs) stored in the unit arms room was that during inventories, every single personal weapon is inventoried along with the assigned military weaponry. The Commander and his armorer are responsible for ALL weapons in the arms room. This is the point where your very nice and expensive bullet launcher is going to be taken out of its storage case (to verify serial number).
Whomever is tasked with that month's inventory is going to potentially play around with it. Imagine some imbecile one-hand snapping the cylinder in and out on a personal Colt Python...or dry firing your expensive shotgun...or simply tossing it onto a metal table top or rack and scratching the finish.
