Highest ranking Allied officer was British Admiral Sir Thomas Spencer Vaughan Phillips. He was in command of Force Z in the Pacific theatre (Battleship HMS Prince of Wales, Battlecruiser HMS Repulse, and four destroyer escorts). He went down with the HMS Prince of Wales when it was sunk by Japanese aircraft.

Highest ranking Axis officer would have been Admiral Isoroku Yamamoto of the IJN, who was commander in chief of the Japanese Combined Fleet. He was in an aircraft shot down by an American P-38 piloted by 1st Lieutenant Rex T. Barber. This was a targeted attack (arguably an assassination) called Operation Vengeance. Yamamoto was chiefly responsible for the attack on Pearl Harbor, and his itinerary had been intercepted by U.S. intelligence (who had cracked the Japanese naval codes), so the U.S. pilots knew where and when he'd be in the air.

Admiral Sir Thomas Spencer Vaughan "Tom" Phillips GBE, KCB, DSO (19 February 1888 – 10 December 1941) Died aboard HMS Prince of Wales When the ship was sunk by Japanese Bombers on the date listed above.

Colonel General Mikhail Petrovich Kirponos (12 January 1892 – 20 September 1941) of the Red Army was also 4-star rank when killed defending Kiev. In 1943 Colonel General became a 3-star rank so is generally considered to be equivalent to 3-star rank when comparing seniority although the rank doesn't translate directly.

For France

Admiral Jean Louis Xavier François Darlan (7 August 1881 – 24 December 1942) assassinated by Fernand Bonnier de La Chapelle a monarchist opposed to the Vichy government. Darlan would be considered 5 star. His association with the Vichy government and his surrender of French troops during operation Torch make him difficult to assign to either the Allied or Axis camp.

For the Axis.

Marshal Admiral Isoroku Yamamoto (April 4, 1884 – April 18, 1943) of the Imperial Japanese Navy. Shot down in an assassination mission by US planes on the date listed above. Rank is roughly equivalent to 5 star making him the highest ranking officer killed in combat during the war

Nobody's mentioned Italy yet, so I'll take a swing at it.

A little more than two weeks after Italy entered the war, Italo Balbo, Italy's Air Marshall and C-in-C of Italian North Africa, was accidentally shot down by Italian AA gunners over Tobruk. His plane was misidentified as one of the British planes that had attacked the airfield mere minutes before. Along with the anti-air emplacements, the airfield was being protected from air attack by the cruiser San Giorgio. Balbo's flight never had a chance after the cruiser and the airfield opened up with everything they had.

Zhang Zhizong, a full general who commanded a KMT army group of eight divisions, was killed fighting the Japanese in Hubei Province in 1940.

Surrounded by the Japanese, his forces had refused either to retreat or to surrender. In the ensuing hand-to-hand combat, General Zhang had been wounded seven times in all, by grenade, bullet, and finally by bayonet. The victorious Japanese realized Zhang's identity only when a major discovered, in the left breast pocket of his blood-soaked yellow uniform, a fine gold pen engraved with his name. The major quickly summoned senior officers; they ordered a stretcher brought and the body was carried away from the battlefield.

Source: http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=2710328&next=true&jid=ASS&volumeId=30&issueId=04

In the closing days in the Battle of Okinawa, Lt. Gen. Simon Bolivar Buckner Jr. (son of the famed Confederate General) was killed by Japanese artillery fire while inspecting troops on the front line, making him the highest ranking U.S. military officer killed in the war. Just the day after, Brig. Gen. Claudius Miller Easley was killed by enemy machine gun fire.

Thank you for all these answers. We covered all the major sides besides the americans and the french. How about those?

Thank you

General Zhang Zizhong might qualify as one of the highest ranking Allied generals to be killed in action. At the time of his death in May 1940, Zhang held the rank of general second-class (equivalent to an American lieutenant general), but Chiang Kai-shek posthumously promoted him to a full general. Of course, the Republic of China did not join the Allies until December 1941.

General Maurice Rose, Divisional commander of 3rd Armored Division. US Army WW2. Highest ranking American officer to be killed by enemy small arms in actual combat. April 1945. Paderborn Germany. American and German armored forces got twisted around each other and while Rose tried to get his jeep back to his lines several German King Tigers cut the road. While being held at gunpoint and ordered to surrender, he was machine gunned by a german soldier in the turret of the lead tank. Conflicting reports as to the actual facts, some witness say he went for his sidearm, others state that Rose was trying to surrender, but the German was yelling at him in German, while Rose was yelling back in English and in the confusion someone let of a burst of gunfire.

As far as the Germans are concerned (since no-one's posted about them yet), one could argue that Rommel was assassinated, but that's playing with the spirit of the question. Barring that, Generaloberst Werner von Fritsch was KIA during the seige of Warsaw.