There are two major storms that come to mind.

The first is known as the "Surprise Hurricane" which occurred on July 25-29th, 1943 in the Gulf of Mexico. This storm is notable for a couple of reasons. One is that it's the first known instance in which an aircraft was intentionally flown into a hurricane, which began the practice of hurricane hunting.

Col. Joe Duckworth, who was known as the father of modern Instrument Flight Rules, was helping to train British pilots at Bryan Field in Texas. Upon receiving news that a hurricane was incoming from the Gulf of Mexico, Col. Duckworth made a bet with other pilots that he could fly his aircraft (an AT-6 Texan) directly into the storm and return safely. He then enlisted the help of the only navigator at the airfield, Lt. Ralph O'Hair. Col. Duckworth then proceeded to fly into the hurricane without asking for or receiving permission for his flight, as he believed it was unlikely approval would be granted. Upon his return, Lt. O'Hair disembarked while a Lt. Jones-Burdick requested permission to fly back into the hurricane with Col. Duckworth. Col. Duckworth then successfully flew into the hurricane and returned to base.

The storm is also notable in that wartime censorship resulted in weather advisories to be released far later than they normally would have, as the U.S. Government was wary of German U-Boat's operating in the Gulf of Mexico using that information. When advisories were ultimately released, they excluded forecast information that might have been beneficial for storm preparations. After the storm came and went, the U.S. Government continued to enforce news blackouts on the aftermath of the storm, so that Axis forces could not ascertain any loses in war material production along the Gulf Coast. News about the ultimate toll taken by the storm was allowed, but only by news outlets in Texas and Louisiana. Ultimately, the storm's destruction resulted in $17 million dollars worth of damage and 19 fatalities.

The other notable storm that comes to mind is Typhoon Cobra, also known as Halsey's Typhoon, which occurred on December 14-19th, 1944 in the Philippine Sea.

At the time of the typhoon's formation, USN Task Force 38 was operating in the Philippine sea conducting raids against Japanese installations in the Philippines. The task force was attempting to refuel their ships at sea in order to continue operating against the Japanese without having to return to port, when weather conditions began to worsen. As the weather worsened, refuelling operations were suspended, however the Task Force remained on station to ride out the storm rather than depart the area.

The storm ultimately resulted in the loss of three destroyers, nine damaged ships, and over a 100 aircraft that were either damaged beyond repair or washed overboard. 790 sailors were lost as well.

Afterwards, an investigation was launched as to why such an avoidable but devastating event was encountered by the task force. It was found that Admiral Halsey wasn't provided with adequate information of the typhoon's strength or location. Admiral Halsey wasn't formally sanctioned for his decision to ride out the storm, but the next month he relinquished command of the Task Force to Admiral Raymond Spruance.

This also led to the the US Navy making greater strides in their meteorology reporting and the eventual formation of the Joint Typhoon Warning Center. Admiral Nimitz later remarked that the typhoon's impact was the equivalent of a major action against Japanese forces.

Further reading:

Halsey's Typhoon: The True Story of a Fighting Admiral, an Epic Storm, and an Untold Rescue

/u/coinsinmyrocket has done a wonderful job covering the two that fit the time period. Because of this, I'm going to go a little bit afield... specifically, to October 8th, 1945 and Typhoon Louise.

Louise started life on October 4th in the Caroline Islands, and for the next few days moved roughly Northwest and was expected to pass between Okinawa and Formosa on its way to the China Sea.

The morning of October 8th, Louise showed the danger of all Oceanic storms, their tendency to move capriciously. It changed course almost at right angles to its original path, a course that would take it about 150 miles south of Okinawa. At that point, US Navy Meteorologists predicted winds of 70mph with gusts up to 100mph, or a Category 1 Hurricane on today's Saffir-Simpson scale (if the Saffir-Simpson was used for typhoons in the Pacific, but I digress).

Except Louise didn't do that. Instead, when it was almost directly south of Okinawa, it came almost to a dead stop and gained strength. You can guess what happened next: it turned north to a course that would bring it within 15 miles of the island.

That's when the trouble really began. There were hundreds of ships gathered at Okinawa. These craft, ranging in size from Higgins Boats up to Victory ships, were sent there in preparation for the now-cancelled invasion of Japan. They had hunkered down at anchor, expecting some stiff winds but that's about all. Now as Louise had changed course, they wouldn't be able to get out of the way.

By the time the storm reached its peak at Okinawa, it was really a coinflip as to whether it was a Category 3 or a Category 4 hurricane, with steady winds ranging anywhere between 115mph and 130mph. Visibility in Buckner Bay, where the fleet had anchored, was effectively zero, there were 35 foot waves, and chaos reigned among the ships.

On land, the situation was quite possibly worse. By the time the storm had passed, about 80% of all housing and buildings on Okinawa had been destroyed, food stocks had dropped to a 10-day supply. 60 or so airplanes had been damaged to some extent, though only a few were outright destroyed. Runways had been damaged by water getting underneath and breaking up the surface. Tragically, the medical facilities on Okinawa had been hit so badly that a Navy hospital ship had to be sent to serve until the situation stabilized.

Out in the harbor, 12 ships had been sunk, 32 had been damaged to the extent they'd need major repair facilities, over 200 had taken damage or blown ashore. Many of these were never repaired, either due to the severity of the damage taken or because the war was over.

Casualties were, on the whole, surprisingly light. 36 men had died, another 47 were missing, and another 100 had suffered serious injuries.

All of this was bad enough, but it would have been much worse if Japan hadn't surrendered and the invasion of Japan gone ahead. The invasion had been scheduled for November, and Okinawa was to have been perhaps THE major staging point for the ships that were going to be involved.

Japan had been saved by the "divine wind" twice before in its history. That very nearly occurred a third time.

It was not a hurricane but on June 19th 1944 Normandy for hit by a massive storm that destroyed one artificial harbor and damaged the other and slowed the allied buildup.