If we need to be specific, let's say in the Pacific theatre. I was taken by surprise when the game World of Warships introduced carrier-launched attack aircraft armed with rockets. I've since learned that rockets a) were used and b) could be reasonably effective, but I have trouble imagining flights of rocket-armed planes during WWII (I usually think guns, bombs, torpedos). So I'd love to know more about how widely they were used. Thanks!
They were very widely-used by Allied carrier-based aircraft during the war. Rockets were used by naval aviators for:
Let's look at a few examples of rockets being used to suppress enemy flak.
Action of October 24, 1944:
During the opening moves of the the Battle of Leyte Gulf, American aircraft from Task Group 38.4 (including the USS Essex and the USS Enterprise) stumbled across the IJN's Southern Force. The Japanese have two battleships, the 39,000 ton Fuso and Yamashiro, supported by a cruiser and four destroyers. American aircraft flying in the area raced to the scene. Within minutes, the Americans had a dozen SB2C Helldivers armed with two 500-lb bombs and sixteen F6F Wildcats armed with 5-inch HVAR rockets.
Barrett Tillman's Enterprise describes what happened next.
From ten miles the battlewagon's main batteries fired fused rounds, bursting at 12,000 feet. Spectacular explosions detonated within 500 feet ... of the aircraft, erupting in red, blue, yellow, and white flashes. The long-range anti-aircraft fire was surprisingly accurate, causing some fliers to flinch in their cockpits. The phosphorus rounds impressed everyone over the ships that morning...
[Emmett] Riera lead the bombers to 15,000 feet while assigning targets... Riera took the lead battlewagon, Yamashiro, sending [James] Moore's team after Fuso, farther astern. As [VF-20 commanding officer] Fred Bakutis lead his Hellcats down to suppress flak with rockets and gunfire, the Helldivers timed their dives to near perfection, plunging on both leviathans simultaneously out of the morning sun. The setup prevented enemy gunners from concentrating their firepower on one group of planes, yielding better survival prospects for the aviators.
It was a sight for the flier to remember all their lives: high-velocity rockets snaking out, bursting on gray steel hulls and superstructure, while bombs left Helldiver bellies at about 2.000 feet. All while the Japanese gunners put up a wall of five-inch flak ... so thick that some pilots could not discern hits or misses on the ship.
SEARCH AND ATTACK (0600-1200)
14 VF, 12 VB - enemy force consisting of the FUSO, YAMASHIRO, 1 MOGAMI class heavy cruiser and 4 destroyers (non well-deck type) sighted and attacked - all units heavily strafed and hit with rockets; at least 5 bomb hits made on the FUSO (large fires started) [in reality, only one bomb hit had been made] and 1/2 hits on the YAMASHIRO plus many near misses - 1 VF plane [an F6F Hellat from the squadron FV-20] shot down by AA, pilot Cmdr. F. E. BAKUTIS, USN (VF-20) last seen in rubber boat [he was rescued by a submarine after spending a week at sea] - 5.5 tons of bombs dropped - 56 rockets fired.
Battle of the Sibuyan Sea (October 24, 1944)
Elsewhere, U.S. Navy carrier planes were fighting an even bigger threat: the super-battleships Musashi and Yamato and the other warships of Center Force.
In his short memoir "Scratch One Battleship," LCDR Charles Dickey recalls taking part in one of the air attacks made against the Japanese battlewagons. F6F Hellcats loaded with four 5-inch rockets helped clear the way for Dickey's torpedo bombers.
...out of the corner of my eye I could see the fighters had reached their targets. Puffs of white smoke beneath their wings indicated they were use their rocket on the cruiser and can [i.e. "tin can" or destroyer] Spurts of flame from the leading edge of wings were fifty-caliber machine guns spitting steel-coated lead into antiacraft mounts and personnel of the screening ships. ... The [cruiser] Mogami broke into flames as five-inch [HVAR] rockets pounded her fantail and fifty-caliber slugs raked her from stern to bow. The [destroyer] Terastsuki exploded violently amidshipas a salvo of rockets found its mark among torpedo tubes. Smoke poured from her center, and lesser fires broke out to make her an inferno of twisted wreckage. Gun crews, unable to stand the fury of the Hellcats deserted their recoiling guns and scurried for futile safety.
Barrett Tillman describes one of Enterprise's attacks on the same ship.
[A] three-dimensional offensive pattern had been crafted to present the two-dimensional defense with an insoluble problem: in very limited tie, recognize the developing play and try to counter it before the ball carriers crossed the goal line... Lieutenant Commander Sam Prickett took his torpedo planes forty-five degrees to port while the Hellcats dived the opposite way. The Helldivers pressed ahead to the pushover point, presenting Kurita's gunners with a three-axis threat Settled into their runs, the bombers dived from overhead, the fighters from the southeast, and the torpedo planes turning in from southeast. The Japanese gunners--hundred of then on dozens of ships--were presented with bewildering arabeqsue of assailants from high above, from medium altitude and most from sea level; from port and starboard.
Joe Lawler, a division leader in the attack recalled:
"From about 176,000 feet, we pushed over rapidly and settled in about 60 degree dive. As soon as I could get the sight on the cruiser, I opened fire with six gens, firing short bursts all the way down .... At about 3,500 fee the ship looked big in the gunfight ... and I salvoed six rockets. I could see some people manning exposed antiaircraft guns, all shooting like crazy."
Enterprise's fighters prioritized the enemy escort ships spitting flak at the incoming aircraft. Within five minutes, the attacking Hellcats had fired sixty rockets and shot up at three of the Musashi's escorts.
The next day, Enterprise would launch four airstrikes against the carriers of the Japanese Northern Force. Some pilots flew two or even three strikes in a single day, with just 45 minutes of rest between sorties. All in all, her air group would expend 12 torpedoes, 107 rockets, and a full 27,000 rounds of machine gun and cannon fire.