This project took much longer than I expected, so I apologize. I'm hoping, however, that my thoroughness will make up for it.
I needed to select some standards for the hashtags so that I could narrow it down to the major five for each decade, since I could easily come up with more than that (for some decades: other decades I could barely get to five).
The first problem I ran into was that Twitter would never really have a decade-long trending hashtag. Major events rarely trend for very long on Twitter. Instead, we get things like, "#JustinWillAlwaysBeTheBest," "#sorrynotsorry," "#43MillionBeliebers," or "#MyFavoriteSongWillAlwaysBe." None of those are particularly noteworthy trends that reflect an entire decade. (You could argue that it really does reflect our decade, but that's not my point right now.)
So, the first priority was that the event needed to happen during the entire decade, multiple times during the decade, or make a significant impact on the world.
The next priority was a focus on international issues, since the decade didn't just happen in the United States. However, United States was second after international issues. The problem I ran into was deciding between political events and pop culture. To be honest, pop culture would be more likely to trend on Twitter. I made an effort to include pop culture when I could, but since your example hashtag focused on the historical, I did the same.
Some hashtags are reflective of the standard Twitter hashtags, while others are simply descriptive. Yay for consistency (or the lack thereof)!
Let us begin!
#naturaldisaster — While containing just as many natural disasters as many other decades, 1900 - 1909 was filled with a number of notable disasters. Most remembered are the eruption of Mount Vesuvius in 1906 and the San Francisco earthquake in the same year.
#snapshot — The Brownie camera was invented in 1900 and made it more financially possible to take pictures. Instagram was on its way to existence.
#phonograph — This technological marvel (for the time) was in widespread popularity, making it possible to have dance parties in your home without hiring an orchestra!
#firstflight — The Wright Brothers made their flight at Kitty Hawk, the first truly verified "first flight." There were other claims, but most aviation historians don't put much stock in them.
#radioactive — No, not the Imagine Dragons song. Marie Curie greatly contributed to research into radioactivity and went on to win two Noble Prizes for her efforts.
#assassination — This decade held a handful of very notable assassinations, namely: Archduke Franz Ferdinand (essentially launching World War I), George I of Greece, and Nicholas II and his family.
#WWI — This is fairly self-explanatory. "The War To End All Wars" defined the decade and set the stage for the years to come.
#sinkingfeeling — The sinking of both the Titanic and the Lusitania left a total of nearly three thousand people dead in their respective crashes.
#cubism — Pablo Picasso, among others, helped to influence the art world to a whole new level.
#igottafever — And it's not Beiber fever. The Spanish influenza epidemic (which I used as a plot point in a short story I wrote in seventh grade) killed millions worldwide.
#YOLO — Sorry, Millennials, the Roaring Twenties had this attitude before you did.
#dryspell — Prohibition went into effect with the 18th Amendment to the United States Constitution, outlawing the sale, production, and transportation of alcohol. This ban lasted through the entire decade, leading to the rise of organized crime and people like Al Capone.
#monkeybusiness — The "Scopes Monkey Trial," as it was so called, brought the debate between creationism and evolutionism to the forefront of American minds and whether or not either should be taught in school.
#lostgeneration — The hipsters of the twenties, the term was typically used to describe those who had been through World War I and struggled to find themselves in the aftermath, particularly American artists, poets, and writers living in Europe. The Fitzgeralds, Ernest Hemingway, and John Dos Passos were among the most notable of the "Lost Generation."
#womansuffrage — This had become a major international issue during this decade, especially as women gained rights during 1920 in the United States and 1928 in the United Kingdom.
#greatdepression — An economic downturn never affects just one country, and the Great Depression was no exception. As you noted, this impacted the entire decade, and was an obvious choice for this set of five.
#nazism — The rise of Nazism took place during this decade, cementing the inevitability of the forthcoming war. Kristallnacht, a devastating attack on the Jewish populations of Germany and Austria, took place in November of 1938, sending thousands of Jews to concentration camps.
#dustbowl — The "Dirty Thirties," as it was so called, was a series of violent dust storms in the prairie lands of the United States and Canada. A combination of extreme drought and lack of crop rotation had a crippling effect on not just the the region, but the entire country.
#hollywood — The decade of the thirties was often referred to as its Golden Age. Hollywood took advantage of people's disenchantment with reality and provided an escape from the problems of the Great Depression.
#wartime — Taking a step back from America, we find that there were actually quite a few wars going on during this decade. The Second Sino-Japanese War (beginning in 1937) was a huge deal, and the Spanish Civil War found the country in a dictatorship. Additionally, there was a war between Colombia and Peru going on, as well as a war between Bolivia and Paraguay. Oh, and the Chinese Civil War.
#WWII — Like World War I, I feel the choice of this hashtag is fairly self-explanatory. The war pulled the United States out of the Great Depression, and led to the generation of baby boomers.
#decolonization — Within this decade, Iceland declared itself independent from Denmark, India and Pakistan from Great Britain, Indonesia from the Netherlands, Syria and Lebanon from France, and Burma from Britain as well.
#swing — This was the era of swing, at least for the first half of the decade.
#atomic — The dropping of bombs on Japan would change the tide of the war, as well as the world.
#crackthecode — Navajo code talkers, the Enigma cipher: the forties was a time for code making and code breaking, assisted by the advent of computer technology.
#Koreanwar — Tensions between North and South Korea led to intervention by the United Nations. The impact of this war is still notable today, especially in the difference between the two countries.
#TV — The television really took off during this decade, and by the end of it, nearly every American household had a television set. It also meant that 3D movies attempted to lure consumers out of their homes and back into the theaters.
#DNA — The double-helix structure was discovered (mostly) by Watson and Crick. It's hard to imagine a world today without this discovery.
#Sputnik — The space race began with the Russian satellite launch.
#rockandroll — This was the time that rock and roll really took off. Elvis Presley, Chuck Berry, and Johnny Cash are names still remembered today for their impact on popular music.
#makelovenotwar — This phrase epitomizes the counterculture and anti-war movement of the sixties. Plus, it sounds like an actual trending hashtag!
#civilrights — A movement that peaked in the sixties, it shook up countries all across the world. African countries, Canada, the United States, Ireland, Germany, and France all found themselves rethinking the rights of minority populations.
#planecrash — At least seven extremely deadly plane crashes happened throughout the entire decade, crashing on nearly every continent. Definitely meets the international requirement.
#spacerace — Following JFK's challenge to put a man on the moon by the end of the decade, it was a competition with the Soviet Union. One that America won.
#beatlemania — According to yayfulness, I can't have the sixties without the Beatles. So, instead of Bieber fever, we get Beatlemania. And people still remember the Beatles. Only time will tell if they remember the Biebs as well.
#stagflation — While it wasn't as significant of an economic downturn as the Great Depression, the combination of increased inflation and unemployment rates let to a distressing economic state in the United States.
#oilcrisis — Occurring twice in the decade, it sparked an interest in developing alternate fuels after the realization that the possibility of running out of fuel became more clear.
#coldwar — Even though this began well before the seventies, I needed to include it in some decade, and this was just the decade I put it in. Not to mention all of the movies it inspired (War Games is delightfully cheesy), this defined American foreign relations for years.
#discofever — Think of the seventies, and you think of disco fever. The Bee Gees, Village People, and ABBA all found themselves amidst the popular music.
#videogames — Ever played Space Invaders? Pong? Snake? Breakout? Oregon Trail? You've played games from the seventies. Don't tell me video games didn't have an impact.
#justsayno — Nancy Reagan's pet project's slogan is reflective of the war on drugs that America began to attempt to fight. It's still going on now.
#crash — Multiple plane crashes, the crash of the Challenger, the Exxon Valdez incident, and the Chernobyl disaster filled the decade with memorable heartaches.
#MTV — Music videos took off, majorly impacting the industry. Michael Jackson, Madonna, and Whitney Houston (among others) helped establish the new format and bring about a genre of music that would become classic.
#irancontra — This was a political event that shook up the eighties, providing a wave of controversy that would have ignited the Twittersphere.
#VHS — The debate between Betamax and VHS would have an impact into the future years as VHS eventually won out.
#dotcom — The internet boom in the nineties would lead to the bubble bursting in the next decade. Regardless, the impact that it had affected the internet and the culture for years to come.
#prayers4 — Followed by either "Rwanda" or "Columbine," as both events were tragic and called for the sympathies of the world (or country). Both of them helped to create changes in how to handle genocide and school shootings.
#billandmonica — The Monica Lewinsky scandal could hardly be ignored in the Twittersphere. While this one may not have had as many lasting effects, it still is a significant part of the nineties for many Americans.
#eurounion — The only truly political event on this list, the formation of the European Union has shown its influence to today, since it still exists. The merits of which are, of course, debatable.
#RIPPrincessDi — Dubbed "The People's Princess," her death was met with an enormous public reaction.
#florida — The controversy over the presidential race between Al Gore and George Bush would inflame the nation as people heatedly discussed their opinions on the matter.
#twintowers — The events of 9/11 would bring a nation together as it kickstarted a discourse on terrorism and the course of action to take against it.
#harrypotter — As I'm personally a child of the Harry Potter generation, I had to include this. The books, movies, and surrounding magic will live on in the hearts of those who grew up reading about the adventures of Harry, Ron, and Hermione. Not to mention all of the children who will be raised with the same stories.
#waronterror — Since the events of 9/11, the War on Terror has been used to describe efforts in Iran, Iraq, and Afganistan, as well as new regulations concerning flight.
#outsourced — Jobs really began to be relocated to other locations around the world, especially India. Not only were these simply factory jobs, but tech industry jobs began to relocate as well.
#Hindenburg — Crashed in the 1930s
#doctorwho — Started in the 1960s, on the same day as the JFK assassination.
#startrek — Also started in the 1960s. You didn't know I was a Trekkie?
#psychedelic — Number one word to describe the 1960s.
#chomsky — Little bit of linguistic favoritism here. Really started to discuss theories in the 1970s.
#starwars — First episode appeared in the 1970s. Don't tell me it hasn't made an impact on pop culture.
#stampede — There were 29 human stampedes in the 1990s.
Shout out to Wikipedia's decade pages for providing me with concise summaries of the decades from which I could select my hashtags!