Psychopaths are generally thought to exist in a low percentile of the population (but no lower than 1 per cent, and potentially double or triple that). Given that their syndrome affects a larger segment of the population than schizophrenics, and given the wide coverage of the subject in academia, popular culture and the media, it would be wise to know when you've met one.
"What is a psychopath?"
An article here talks about how a psychopath views the world, and how they interact with the rest of society. In essence, psychopaths are like "psychological vampires", but no two psychopaths may be the same. While there are a common set of personality behaviours and characteristics, Kevin Dutton suggests that "psychopathy" operates on more of a "sliding scale", and with a "mixing deck" of attributes.
Generally speaking, we can isolate a number of stand-out characteristics that together may allow someone to suspect they have encountered a psychopath:
Psychopaths are known for having a lack of the normal range of human emotions. While a normal person displays a range of emotions throughout the day, psychopaths are instinctively unable to reproduce it. They may well be able to successfully mimic (more on that later), but psychopaths naturally have "a predator's eye". Past victims of psychopaths, once they become aware to the reality of who they are dealing with, have told of the emotional "emptiness" they see in the psychopath's eyes. They see the world in a different way to a normal person, and more in the style of a predator hunting his prey. Related to this is the fact that psychopaths are naturally very cool under pressure; which explains why they tend to disproportionately exist at the top end of business and society. It also means they can make decisions unclouded by emotional attachment. This lack of empathy also means that they are easily capable of acts of sadism that a normal person would have grave hesitation about doing, ranging from a "psychopath CEO" coolly firing half of his staff without notice, to someone in a position of high office ordering mass murder.
A natural charmer
One thing that many people in the know can agree on is that psychopaths are charming and charismatic. Funny, persuasive, and manipulative, psychopaths know how to get what they want. They are easy talkers, often being able to even charm their own interrogators when in custody. Having such skills, they can usually talk their way out of any compromising situation (often to the astonishment of others: "how did he get away with that?"), while similarly being able to talk up their attributes into getting promotions or favours far beyond what they actually deserve.
Lie, and lie again
Psychopaths are typically pathological liars. Often their lies come out instinctively. They will shamelessly lie to get what they want, or to get out of an awkward moment. When their lies are found out, they will spin the lie into something entirely new, or make their interlocutor feel like they're going crazy as the psychopath pretends that the lie never existed in the first place. Used in conjuction with their persuasive and manipulative charm (see above), it makes the psychopath a very difficult individual to pin down.
Rules are for other people
Psychopaths use their skills to get away with doing what they want, when they want. They believe that "rules" are for someone else, and that anyone who doesn't understand that they are "special" or "different" from others is just stupid (see narcissism). Bystanders and colleagues will usually be stunned by the amount of shocking and disruptive behaviour a psychopath will carry out; this can include practically anything, including actions at the workplace that would normally be sufficient for dismissal. At the worse end of the scale, of course, such people may also be serial adulterers, violent, etc.
A high sex drive
While it's not always clearly stated, psychopaths like sex, and usually with lots of different people over a period of time. Tying in with the idea that they are moral vacuums, psychopaths are "charming bastards" that like to play around with sex. Like the narcissists they are, they treat their sexual partners as objects of gratification, to be explored, used, and discarded without a moment's hesitation when things get too "difficult" for them. A "well-adjusted psychopath" may well be satisfied with serial adultery after carefully choosing a suitably-pliant wife (or if he's very lucky, a partner with similarly loose ideas); in the middle range of things, another psychopath will shamelessly bounce from one woman to the next; in the worst case, a psychopath can be a serial rapist or worse (see Jimmy Savile and former rock singer, Ian Watkins).
"I invented the piano-key neck tie!"
The quote above is from a funny scene from the comedy film "Zoolander", where the character Mugatu (a fashion king) angrily loses his patience at others' perceived failings. It's a silly scene, but reminds us of how crazily narcissistic a psychopath can be compared to others. Psychopaths usually have completely unrealistic notions of how they are perceived by others, how their lives will be perceived, and of their future ambitions. It's not unusual for them to think it a realistic aim for them to be a future statesman or athlete, in spite of their complete lack of qualifications or planning. But their lack of planning leads to another related attribute...
Plans are for losers
Psychopaths change their ideas frequently, and rarely think far ahead into the future. There are documented cases of psychopaths, whose long-suffering partners listen to their ideas for making millions suddenly appear from nowhere, only to disappear again a short time later, to be replaced by some other "great idea". In this sense psychopaths ideas seem to rest on bursts of activity, only for them to quickly get bored of the idea or the actual work required ("boredom" is another thing that a psychopath suffers from). This explains at a more prosaic level why psychopaths jump from one sexual partner to another, jump from one job to another, or suddenly decide to completely change the direction of their career, or even where they live. This lack of planning also relates to how they often get into trouble when their many lies catch up with them (by failing to think ahead). Impulsiveness naturally stems from this behaviour as well.
Anger management problems
Relating to the idea of impulsiveness is the fact that psychopaths have low levels of control of their temper. While psychopaths cannot be said to have "real" emotions, they do have sudden bursts of "contrived" emotion when suitably provoked. The provocation may be something seemingly trivial, but to the psychopath, that "trivial" event (in his mind) may be seen as something deadly serious. A psychopath is capable of lashing out seemingly for no reason; in the worst case, killing at a whim, or without any real control of his own actions (being "ruled" by a sudden flush of temper). This behaviour indicates a person who is not following (or capable of following) the normal rules of society, and is a potential danger to those around him.
A leech on society
Lastly, psychopaths are famous for their parasitic lifestyle. In other words, they are talented for living off the efforts of others. Using their various skills (as described above), they are able to wheedle money, food, accomodation, sexual favours, or other "benefits" from people they encounter. While all of us may do this from time to time (when the situation demands), psychopaths make this a habit, and some of them use it practically as a survival technique.
Interestingly, while the vast majority of psychopaths are men, a small proportion of them are women. While female psychopaths may well have the same "core" attributes to male psychopaths, a female psychopath may well use her attributes and sexuality in a manner different from a male psychopath (and for different ends), due to their physical and biological differences. Cultural assumptions (and playing to stereotypes) may also play a factor.