This is the details of a realistic campaign set in a parallel to the modern world where a very small number of people gained highly focussed super-powers, starting in 1920 or so, with increasing numbers appearing every year. It has been run with the HERO system, but there is little that is system-specific here.
The concept is similar to (although predating) the Wild Cards series of stories, but the feel is quite different. Wild Cards is an open-ended setting for dramatic short stories. In this world, almost everything is linked in an ongoing saga. The paranormals are not random victims of a virus, but rather a mysteriously select few. They are neither costumed crimefighters or regular guys with powers, but instead strong-willed individuals with their own agendas.
The campaign is grand and encompassing, with lots of room for scheming, investigations, and paranoia.
Those affected had a lot in common. One, they all gained their powers between the ages of 10 and 25 or so. Two, starting in 1913, they all appeared in the vicinity of England, until 1955, when they began exclusively appearing in the North-Eastern United States. They appeared in increasing numbers over time, but in total, no more than 150 or so appeared - and most of these were after 1960.
More importantly, all of them had certain personality traits in common: they were highly intelligent, competant, and self-willed. They were generally curious by nature - poking into any sort of secrets and activities they could find.
Overall, most tended to work on both sides of the law. Neither Britain nor the U.S. changed the laws for such a handful of people, so often their activities were 'extra-legal'. They tended to keep their powers a secret due to the potential for various hassles. (This had somewhat to do with their common personalities, otherwise I would imagine that several would go into show business, gathering lots of fame and fortune).
They tended to acquire money from a variety of sources - few of them steady, 'honest' jobs. Often groups, universities, or the government bureaus were willing to pay fees for studying their powers, for example. Many other one-time jobs were considerably less legal - for intelligence agencies, criminal groups, or others.
On the types of powers they had: most were one-sided, like Mark Charlton who became invulnerable to harm. A lot of energy manipulators, like Paula Bell who could project very strong magnetic fields. Notably, there were no known people with mental powers - those who had them were smart enough to realize that no intelligence agency or secret organization in the world would suffer such a creature to live.
In Britian there was a certain paranoia about the problem at first - the first paranormal to reveal his powers did so escaping from police custody in 1921. However, this was avoided later as someone organized the Paranormal Studies Institute of London - which worked with the government on some points (and against it on others). Several paranormals fought in WWII, which had little tactical effect, but did help morale a lot.
Pretty soon, it was business as usual - like most oddities, they fueled some books and tabloids - but no major social effects. Then two things happened: first, someone with nuclear manipulation powers appeared in 1952 in Middlebrough, and inadvertently caused a lot of havoc and fear before he was killed by government agents. The next year, paranormals started appearing in the United States.
This led to a government crackdown on paranormals, conducted out of the public eye - which attempted to track the movements of and actively recruit paranormals. Less was seen of many older paranormals, and many tried harder to give the appearance of being useful, social citizens (and conceal their other activities). Unfortunately, more and more of their secret activities came to light - many disappeared, slipping out from the governments eye. A clairvoyant, Paul Badrov, in the U.S. was prosecuted for invasion of privacy, and sentenced to public service with the government.
During this time, there was a lot of effort to avoid using actual facts in media portrayals of paranormals - which many people gladly cooperated with. Their image was somewhat sugar-coated, but then, fewer people actually believed it (and they also ignored many rumors which were true).
This eventually led to various attempts by the FBI and CIA to find things for those who they could recruit to do. An ill-fated attempt to use some recruits in Vietnam ended in 1968 with most quitting in disgust, and notably Paul Badrov defected to the Soviet Union (!) for reasons of his own.
This led to a major overhaul and rethinking in the government, and in 1977 the Minuteman project was started by Congress. Officially, it was hiring paranormals to find useful outlets for their powers, and helping other sections of the government. In truth, it was more-or-less a bribe to the few who joined to stay in control, and at least pay attention to laws before they broke them.
Overall, the carrot worked much better than the stick, and many paranormals made an effort to police themselves. A paranormal arms smuggler in L.A. was brought to justice by an independent group, for example, and the Minutemen actually cooperated in a government investigation of a paranormal biochemist.