As far as the Pacific goes its actually a bit more streamlined at least when it comes to the VF fighting squadrons that served aboard the USN's carriers during the war. And we have a mostly clear progression between 3 airframes, the F4F Wildcat, F6F Hellcat and F4U Corsair, and distinct phases and preferences for each aircraft.

And of the 3 we can say that the F4F Wildcat saw the longest service afloat, serving from the start of the war until the end, and making up the majority of those in service until the summer an fall of 1943. From there the F6F Hellcat dominated the carrier forces VF squadrons, while the Corsair was beset by a frustrated development, and was initially relegated to shore based squadrons(including famous service with the Marines) and was only reintroduced to carrier groups in early 1945 after the Royal Navy worked out some reforms and its value as a fighter-bomber was proven.

For production numbers its actually rather straight forward, about 8,000 Wildcats of all types were produced, a good number of which were the FM version by General Motors. After the introduction of the Hellcat and Corsair the Wildcat saw new life as the fighter aircraft aboard the smaller, slower escort carriers, and while Grumman transitioned to other types GM took over continuing the production line.

While about 12k Hellcats and Corsairs were produced for both types, though Corsair production was over a much longer timeline. The final batch was an order for the French Navy which was delivered in 1953! And following WW2 the Corsairs which remained in USN and USMC service were mostly dedicated specialist variants, attacker, night fighter, and recon variants for example. While the Hellcat was quickly replaced by the F8F Bearcat and then new jet aircraft aboard carriers.

Unfortunatley Ive never come across the same stats in a nice chart form(and KUDOS if he made it) like /u/Bigglesworth_ has. But we can come close. The USN compiled monthly reports on the location and strength of all its(and the Marines) squadrons during the war.

Just pulling the ones from August of 1942, 43, 44, and 45 to show the changes. We start in 42 just as the invasion of Guadalcanal began. The fighting squadrons are all exclusively F4F-4 Wildcats which introduced the eventual standard armament of 6 .50cal Browning's and folding wings to increase the number that could be carried. Notice too that the report for ALL naval squadrons worldwide is just 5 pages!.

1943 is mostly the same story, those squadrons afloat, namely the Saratoga's air group and those other air wings in theater at Noumea, Espiritu Santo and Guadalcanal or elsewhere in the South Pacific are still flying F4F's. But in all the carrier groups which are at Pearl, on their way there, or forming stateside, the VF units are formed with F6F Hellcats. This represents the coming together of the famed "Fast Carrier Force' which in a few weeks would first be unleashed against the Gilbert and Marshall islands to support the first landings in the great island hoping campaign across the central Pacific. Underwritten by the new Essex class fleet and Independence class light carriers. The report is also now 10 pages long!.

1944 then we see this clear delineation in effect. The most numerous type in service is the F6F, equipping each Fleet and Light Carrier with between 25 and 35 aircraft per squadron. While FM1 Wildcats equip all the Escort Carriers, and the numerous Marine Squadrons and a handful of shore based Navy squadrons fly the Corsair. The report has also bloated to 41 pages.

Then at last in 1945 we see the Corsair serving afloat, but outnumbered essentially 3:1 by Hellcat squadrons(though this was changing in the Corsairs favor and carrier groups of majority Corsair's would see service at the end of the war and immediately post war). While we also see other notes such as the first F8F squadron projected, and F6F's being placed into CVE air groups as well, in part to serve as dedicated night fighter carriers along with the handful of fleet carriers(at this time the pairing of the Enterprise and the Bonny Dick served as the night focused Carrier Division 7). While Corsairs still make up the majority of the USMC VMF squadrons, though they too have some night fighter squadrons equipped with Hellcats. While we can also note that the report is finally leveling out at only 51 pages!

For raw statistics the [Army Air Forces Statistical Digest (World War II)] (http://www.dtic.mil/dtic/tr/fulltext/u2/a542518.pdf) is hard to beat. Table 84 is Airplanes on Hand in the AAF, By Type and Principal Model: Nov 1941 to Aug 1945; just pulling out the figures from January of each year gives an idea of the composition of USAAF fighter units:

Type	Jan 1942	Jan 1943	Jan 1944	Jan 1945
P-38	132	871	1948	2745
P-39	684	1137	2068	665
P-40	1080	2017	2275	1564
P-47	1	378	4349	5011
P-51	2	56	1420	4338
P-59	-	-	-	17
P-61	-	-	31	440
P-63	-	-	36	309
P-80	-	-	-	-
Other	448	208	357	101

As can be seen the P-40 is the workhorse for the first couple of years, the P-39 was also used but never particularly well-regarded in the US or UK and used in greater numbers by the USSR (who were much keener on it) under lend-lease. The P-38 had a fair few teething problems, by the time they were worked out the P-47 and P-51 were the main fighters (particularly in the European Theater). The P-51 came to the fore from late 1943 when the Merlin-engined P-51B and subsequent variants significantly improved high-altitude performance compared to the earlier Allison-engined models; as they arrived in numbers most P-47s in the ETO then switched to the tactical fighter-bomber role in the 9th Air Force. The Statistical Digest has further breakdowns by Theater if you're interested in exactly where most types were employed.

I haven't got an equivalent source for the Navy; very broadly its main fighter in 1941 was the F4F Wildcat, replaced by the F6F Hellcat and F4U Corsair over the course of the war. A specialist like /u/DBHT14 may be able to help if you're after more detail.