The truth is out there…
This world looks very much like the one we all experience; birthdays, taxes, and grinding jobs. In that world, however, there is a secret organization, dedicated to protecting everyone from… something. 
Depending on your game something can be a lot of somethings, or one subtle difference. I have always loved alternate histories–including the old TV show Voyagers. Sometimes the tiniest twist is all it takes to make a radically different reality… if you indulge in some enthusiastic fallout from the actions. Rather than going that route, for now… let’s look at various somethings that can explain our very different setting.
Magic or the Supernatural is Real
This is one of the most popular “somethings”. White Wolf’s settings often followed the formula of “treat this one element as real… how would that group’s reality have altered the world? Elegant worlds spilled out; vampires stylishly lounged in shadowy dance clubs, Mages bent their efforts to control reality, Werewolves engaged in a pyrrhic struggle against the forces of technology and consumption. If you want to uncover a world with Vampires secretly pulling strings, Night’s Black Agents gives you a teetering path.
Call of Cthulhu is a setting much like ours, to everyone’s common view. A few researchers, however, know a much darker truth… and struggle against crazed madmen who worship unspeakable horrors, or who take shortcuts to power with consequences horrible to imagine. (Another great take, with a similar feel of terrible horrors seeking to unmake the world is from the 20 Palace novels, beginning with Child of Fire.)
Aliens Among Us
This setting allows us to keep expectations of physics and science more aligned with the players’ experience. The tone can vary widely; you can go big and silly with your hidden alien tech to wind up with Men in Black, or much subtler and creepier to get an X-files feel. You can even mirror the feel of XCom at the beginning…
These games seem to be ideally suited for generic systems, like GURPS or Fate, since “reality with a small twist” is what these systems default to, and there don’t seem to be a lot of near-future games without a lot of exotic to them. Sure, you could play using Shadowrun for the alien tech… but that’s not what Shadowrun is best at providing.
Truly Normal… almost
Specific game systems can capture a specific feel; Millenium’s End or Aces and Eights stick pretty close to the technologies and challenges of our reality. Blowback is basically reality… just at action movie levels.
With these systems, your conspiracies can be very traditional; you don’t have to explain why anti-gravity hasn’t revolutionized physics, or how the elder ones can come so close to escaping so many times, but never actually eat Chicago.
You can dig into subtler things at this level; if the main difference is that the Civil War came earlier than our history, then you can explore competition between rival Americas. If the reality is the same as ours (the same wars are going on, etc.), then investigating the conspiracy and its goals can be more involved than “Aha, they were trying to hide the existence of Vampires.” Once you see who is involved, as you break down their organization clue by clue… is it significant that they used HSBC to launder their money? Maybe that young politician was treated by brainwashing drugs… or is that just an excuse? It’s a lot harder to tell before the giant pharmaceutical conspiracy is revealed as the villain.
Something: Creepy, Awful, or Reality Based
Picking a foe for your hidden world builds the feel of your setting. It’s what the characters will encounter session after session…
That makes it tricky; your evil organization is often the real recurring villain of your game. Sure, the characters wrestle with Herman Dietrich this episode, and Walter Donovan the next… but the villains prove to be facets of the enemy group, the conspiracy with which they’re engaged in an endless struggle.
Picking a good villainous organization can go several directions, and is almost as influential as the supernatural level of the setting. You can pick a real world villainous group and use it for any setting, however alien or supernatural, by having them clued in (or augmenting their real world power with supernatural servants, or alien tech). This can be tricky, though; trolling the web for narcoterrorism articles can be good inspiration but terribly disheartening–especially if you turn to it week after week for your prep. Similarly, picking truly loathsome groups may have everyone reaching for their X-card; it may feel good to defeat people who enslave children, but exploring the enemy network and encountering those enslaved children could crush the players’ spirits… especially since saving everyone in the nick of time is less common in roleplaying (with dice and chance) than in novels and movies.
What Lurks in the Walls of Your World?
Have you played a modern world, or slightly skewed game recently? What foes loom in the halls of your hidden world? Lay out some recent foes or opposing organizations that you enjoyed in comments!
One of the things I really liked about the Dresden Files RPG (Fate-based) was building the setting. Our group decided to use our own city as the basis, so there was a lot of familiarity with the locales, customs, and people to build on. This led to some fairly subtle alterations on the reality, like changing a gang’s leadership to red court vampires, turning some local legends into fey sightings, and adding a secret ward to the local Sisters of Charity hospital for treating magical/supernatural issues.
As for foes… our most interesting foes are almost always ourselves. I tend to create tragic heroes (and sometimes villains), while another of our group tends to create greedy and egocentric characters, and another tends toward the well-intentioned trickster in over his head. More often we find ourselves sabotaging ourselves without the need for an opponent.
I really like Dresden’s city creation too–and starting with a setting that’s so familiar does make it easier to enjoy the subtler levels. When it’s neighborhood you know getting attacked by the Red Court, it resonates in a way that demolishing small cities of strangers sometimes can’t.
Did your characters accept the status quo, or did they dive into solving things and that’s when your self sabotage came into play?
I’ve wanted to run a game like this for a while now.
I’ve often felt inspired to do an “aliens actually walk the Earth” type of game in the mold of the sixties TV series The Invaders.
Who are these aliens? Why are they here? Do they look like us or are they actually hiding behind a human shell? How many of them are there? Are they hostile? Are other humans working with or for them? How far does their influence go? Why is there a massive veil of secrecy within our own government about this?
That would be a creepy, paranoid setting. It’d be interesting to dig into the problems with only 1960s tech and attitudes…
I think it would be a good idea to set it in the sixties or seventies. No internet. No digital photos. No cell or smartphones.
Alien gadgets would really stand out like a sore thumb considering the tech level. But that was part of the charm with the TV series. Often times people would pick up an alien gadget and have no clue as to what it was for or how to operate it.
A couple of the most memorable campaigns I ever played in used this theme. Both used our d20 homebrew for modern settings. One took place in Seattle, using the magic is secretly real paradigm. All the characters had some level of latent magical ability, except mine, an old-boy-style ex-con who had spent most of his life in Prison, where he discovered a love for literature. Playing the “muggle” of the group was hilariously fun and exciting. Most memorable moment: when my car locked me in and drove of its own accord (as if possessed) out into the wilderness to an isolated old house in the forest, where I found another vehicle containing a corpse and a mysterious leather-bound journal. Exploring the house, which was itself posessed, was probably the most terrifying gaming experience I’ve had.
The other memorable “truth-is-out-there” game I played in was set in a coastal Alaskan town, where all the dogs were dying mysteriously, and a few locals had been traumatized by strange sightings or encounters. What none of us knew, was that shape-changing aliens were gradually replacing the population (the dogs had to die because they could tell!). Most memorable moment: after responding to a family’s desperate phone call for help, we find them afraid but seemingly unharmed. While securing the premesis I notice piles of tarps in the basement, but am distracted by noises outside the house. If only I had looked under those tarps! The real family’s dead bodies had been hastily concealed under them moments before we arrived, the shape-changers upstairs fooled us completely!