A complete list of US aircraft would take up far too much space; instead,
I've listed only the post-war "F" and "A" series, the ones most often asked
about.

One star indicates a type that existed only as one or more prototypes and
never entered service; two stars indicate a type that never left the
drawing board; three stars indicate that the number was never assigned at
all (as far as I could determine).

USAF fighter designations, since the initiation of the "F" series in 1948:

    F-80:  Lockheed F-80 Shooting Star
    F-81:  * Convair XF-81 (experimental mixed-power jet/turboprop fighter)
    F-82:  North American F-82 Twin Mustang
    F-83:  * Bell XF-83
    F-84:  Republic F-84 Thunderjet/Thunderstreak/RF-84 Thunderflash
    F-85:  * McDonnell XF-85 Goblin (parasite fighter experiment)
    F-86:  North American F-86 Sabre
    F-87:  * Curtiss XF-87 Blackhawk
    F-88:  * McDonnell XF-88 Voodoo
    F-89:  Northrop F-89 Scorpion
    F-90:  * Lockheed XF-90
    F-91:  * Republic XF-91 Thunderceptor
    F-92:  * Convair XF-92
    F-93:  North American YF-93 (F-86 derivative)
    F-94:  Lockheed F-94 Starfire (F-80/T-33 derivative)
    F-95:  North American YF-95 (became F-86D)
    F-96:  Republic YF-96 (became F-84F)
    F-97:  Lockheed YF-97 (became F-94C)
    F-98:  Hughes F-98 Falcon (air-to-air missile; became GAR-1, later
        AIM-4)
    F-99:  Boeing F-99 Bomarc (ground-to-air missile; became IM-99, later
        CIM-10)
    F-100:  North American F-100 Super Sabre
    F-101:  McDonnell F-101 Voodoo
    F-102:  Convair F-102 Delta Dagger
    F-103:  ** Republic XF-103 (turbojet/ramjet hypersonic interceptor)
    F-104:  Lockheed F-104 Starfighter
    F-105:  Republic F-105 Thunderchief
    F-106:  Convair F-106 Delta Dart
    F-107:  * North American YF-107 (F-100 derivative)
    F-108:  ** North American XF-108 Rapier (long range interceptor and
        XB-70 escort)
    F-109:  ** Bell XF-109 (but see below)
    F-110:  McDonnell F-110 Spectre (designation used briefly for USAF
        version of F4H/F-4 Phantom II)
    F-111:  General Dynamics F-111 (the common name "Aardvark" is
        unofficial)
    F-112:  ***?  (may have been attached to Russian aircraft)
    F-113:  ***?  (may have been attached to Russian aircraft)
    F-114:  ***?  (may have been attached to Russian aircraft)
    F-115:  ***?  (may have been attached to Russian aircraft)
    F-116:  ***?  (may have been attached to Russian aircraft)
    F-117:  Lockheed F-117 Nighthawk

Note:  Bell applied the designation "XF-109" to a VTOL fighter project of
the late 1950s (one prototype was built but never flew); however, this was
assigned unilaterally by the company, and was not sanctioned by the USAF.
The "F-109" designation has never been officially used, probably as a
result of Bell's breaking the rules.

USAF/USN fighter designations, since the adoption of the Tri-Service
designations in 1962:

    F-1:  North American F-1 Fury (formerly FJ)
    F-2:  McDonnell F-2 Banshee (formerly F2H)
    F-3:  McDonnell F-3 Demon (formerly F3H)
    F-4:  McDonnell F-4 Phantom II (formerly F4H, briefly F-110)
    F-5:  Northrop F-5 Freedom Fighter/Tiger II
    F-6:  Douglas F-6 Skyray (formerly F4D)
    F-7:  * Convair F-7 Sea Dart (formerly F2Y)
    F-8:  Vought F-8 Crusader (formerly F8U)
    F-9:  Grumman F-9 Panther/Cougar (formerly F9F)
    F-10:  Douglas F-10 Skyknight (formerly F3D)
    F-11:  Grumman F-11 Tiger (formerly F11F)
    F-12:  * Lockheed YF-12 (A-12/SR-71 derivative)
    F-13:  *** (never used)
    F-14:  Grumman (now Northrop Grumman) F-14 Tomcat
    F-15:  McDonnell Douglas F-15 Eagle
    F-16:  General Dynamics (now Lockheed) F-16 Fighting Falcon
    F-17:  * Northrop YF-17 Cobra (lost to F-16 in Lightweight Fighter
        contest)
    F-18:  McDonnell Douglas F/A-18 Hornet (YF-17 derivative)
    F-19:  *** (never used, at least officially)
    F-20:  * Northrop F-20 Tigershark (F-5 derivative)
    F-21:  IAI F-21 Lion (leased Kfirs, used as Aggressors in training)
    F-22:  Lockheed/Boeing F-22 Lightning II
    F-23:  * Northrop/McDonnell Douglas YF-23 (lost to F-22 in Advanced
        Technology Fighter contest)

Note:  The Rockwell XFV-12 was number 12 in the "V" series, not part of the
"F" series.

USAF/USN attack designations, since the adoption of the Tri-Service
designations in 1962:

    A-1:  Douglas A-1 Skyraider (formerly AD)
    A-2:  North American A-2 Savage (formerly AJ)
    A-3:  Douglas A-3 Skywarrior (formerly A3D)
    A-4:  Douglas A-4 Skyhawk (formerly A4D)
    A-5:  North American A-5 Vigilante (formerly A3J)
    A-6:  Grumman A-6 Intruder (formerly A2F)
    A-7:  Vought A-7 Corsair II (F-8 derivative)
    A-8:  British Aerospace/McDonnell Douglas AV-8 Harrier
    A-9:  ** Northrop YA-9 (lost to A-10 in AX contest)
    A-10:  Fairchild A-10 Thunderbolt II
    A-11:  ***?  (apparently never used)
    A-12:  ** McDonnell Douglas A-12 (cancelled A-6 replacement)

Notes:  The Harrier seems to have taken the number 8 slot in both the "A"
and "V" series.  The designation A-12 for the original, single-seat version
of the aircraft that became the SR-71/YF-12/M-21 was an internal Lockheed
designation, not an official USAF one (the A-12s were operated by the CIA
and never officially entered military service).  The designation A-37 for
the attack version of Cessna's T-37 was derived from the trainer version of
the aircraft and was not part of the real "A" series.