Forgive me for the slightly morbid question, it's just something I was thinking. I know Hawaii was bombed in Pearl Harbor, although that was before Hawaii became a U.S. state. And of course during 9/11, planes were used as bombs, but that's not the same as a device explicitly designed to explode and kill.
Also discounting things like parcel bombs and IEDs which have been used in terror attacks such as the UNABOMber, the 1993 WTC attack, the Oklahoma City bombing, the Boston Marathon bombing, etc.
Has the mainland United States ever actually had an incendiary device deliberately dropped, from an aircraft, by an enemy of the United States, on any population centres or military base? As a British citizen I'm quite familiar with the concept of incendiary devices being dropped on civilian populations, as London was bombed heavily during the Second World War, and there still exist a few damaged buildings to this day.
I was curious as to whether the US has ever been bombed in this way or if it's somehow managed to escape this.
Yes!
Towards the end of WW2 the Japanese deployed unmanned aerial balloons armed with small (5-15kg) bombs. The balloons (Fu-go in Japanese) used hydrogen as a lift gas, and were launched from mainland Japan when they believed the weather patterns would carry them to North America.
They developed several warheads for these balloons, including explosives, incendiaries and biological weapons.
Many of these weapons made it across the Pacific to Canada and the United States. Many of those exploded. Some of them started fires.
One of them landed in power lines supplying the Hanford site of the Manhattan project, but they had decent redundancy so it had no real impact. This one boggles my mind. Given the colossal area of the North American continent, the odds of one of these balloons arriving at a strategic facility are astonishing.
The existence of these attacks was kept as secret as possible. The primary goal from the Japanese perspective was to cause terror, and the US authorities recognised the need to keep news of the attacks from the public, so the press were censored.
The balloons relied on the jet stream to travel across the Pacific before they deflated. The jet stream had only recently been discovered, and was poorly understood.
Overall it was an interesting weapon, but not very effective.
Try this book for a proper historian's view on this.
In addition to the unmanned balloons mentioned below, the Japanese did launch one air attack on the mainland USA in 1942. A submarine-launched seaplane dropped two bombs on the forests of Oregon, with the intent of starting a major forest fire; however, the fire was quickly brought under control and damage was minor.
However, this was not the first time that the US was bombed!
During the Escobar Rebellion in Mexico in 1929, a battle was fought over the town of Naco, which lies on the American border - in fact this town is divided in two by the border. The anti-government rebel forces hired a mercenary pilot named Patrick Murphy to drop improvised bombs on government troops. However, Murphy accidentally bombed the American half of the town (Naco, Arizona) on several occasions.
The US dispatched soldiers and warplanes to the area, but by the time they arrived, the battle was over and Murphy's plane had been shot down by Mexican troops.
Going even further back, I believe balloons were widely used for observation in the American Civil War, but to my knowledge there's no record of them being used to drop bombs on the enemy. I wonder if they were ever used by snipers, though?
Since no one else has mentioned it, I'd like to tag one other example: The War of 1812.
As I understand it, British historians tend to categorize it as a minor theater of the Napoleanic wars, but in the US and Canada it was considered a full blown war, complete with a US declaration of war against the UK.
Whether this meets your standards as to the definition of "bomb" relies on whether exploding ship-launched explosive device would still count. The phrase "Bombs bursting in air" from the US national anthem uses the term to describe the shelling of Fort McHenry, so maybe it ought to count in some anachronistic sense.
So there is one other incident that is worth mentioning, ignoring for a moment your if I may be honest a little ridiculous distinction of Hawaii's territorial status, we can look again to WW2. This time to Alaska.
As a sideshow to the Midway operation a small task force including a pair of carriers were sent to support Japanese landings on the outer Aleutian Islands. To cover the landings it was planned to attack the primary settlement at Dutch Harbor which also was the location of the primary US base on the chain.
One June 3rd and again on the 4th about 2 dozen IJN aircraft attacked the harbor, port facilities, and military base, doing moderate damage, in part because there simply wasn't much to attack. All told about 80 US Servicemen were killed, in return for the loss of a half dozen aircraft for the Japanese.