And the Earnestians still hold celebrations to that effect.
Off the top of my head:
(This is for U.S. service, only. Some of these may have seen combat with non-U.S. services, but I do not know how many other than the ones mentioned.) This also ignores one-off planes that never made it to squadron service such as the F3U or the F10F.)
FF-1 “Fifi”
F2F
F3F
F8F Bearcat
F11F Tiger (Aside from one shooting itself down)
F7U Cutlass
F8C Helldiver
AM Mauler
MB-3 (first U.S. designed fighter used by Army Air Corps)
P-6 Hawk
F2B
F3B
P-12 / F4B
P-36 Hawk (Some were shot down by the U.S. when flown by Vichy France in the North African operations.)
P-43 Lancer (Used in combat by other countries)
F-101 Voodoo
B-45 Tornado
P5M Marlin (Later SP5 was used in Vietnam, but only as reconnaissance)
I think the French used the F-8F Bearcat in combat in Vietnam.
I thought the F-101 Voodoo had been used in combat in Vietnam, but I read that the reconnaissance version was the only one to see combat; and I’ve excluded unarmed missions.
The F4D/F-6 Skyray, as far as I know.
Very technically, depending on how you define “U.S. combat aircraft” and “never used,” maybe the F-21A. Which I don’t count, and which probably doesn’t count under the OP. But it’s got interesting rules weasel value. 
No, the Kfir is not a U.S. aircraft. It’s an Israeli aircraft that was used by the U.S., much like the F-104 was a U.S. aircraft that was used by other countries.
Those P-26’s are still one of my dream airplanes to own & fly.
…as indicated by my “how you define ‘U.S. combat aircraft’,” “technically,” and “weasel” comments. 
Oh, those combat their own pilots 
You guys are all forgetting the Spruce Goose.
(Runs and hides.)
I disagree with including the YF-12. The Y prefix indicates it was a prototype, as in “NOT IN SQUADRON SERVICE”, so I don’t consider it an official U.S. combat aircraft.
It was a transport, not a combat aircraft.
It likely doesn’t count, but I have a soft spot for the Douglas XB-42 Mixmaster.
Hooooo-eee! That is one fugly plane.
Really, really fast for a prop plane, though. If not for jets, it would have been a front-line bomber.
Speaking of jets, the Bell P-59 Airacomet. Kind of 1930s sexy although not a super performer.
A handful of P-36s got off the ground at Pearl Harbor and were credited with a couple of Zekes, but that’s it for US service.
It’s not without competition. The YFM-1 never saw combat either
If you modify that to read WWI and the mid thirties, it’s a whole lotta types. P-16 for example.
I’m having trouble verifying that the B-50 ever saw combat in Korea. The B-29 certainly did, but it looks like the B-50 may have stayed parked, waiting for the war to go nuclear.