Powergamer
"Powergamer" is a term describing players who are interested in winning and, more to the point, winning big. Exactly how they do this depends on the game.
Powergamers who play RPGs generally attempt to make their characters as effective as possible within the game mechanics, possibly (but not necessarily) by exploiting broken or badly worded rules. The term is usually used pejoratively, suggesting that the player in question only cares about the mechanical power of their character and this comes at the expense of roleplaying, although there is nothing intrinsic to powergaming that inhibits good roleplaying.
In Magic: The Gathering, powergamers are also called Spike or "Spikes", a name chosen specifically because it sounds all Serious Business and boring.
In wargaming: powergamers are less likely to be referred to as such due to it's association with level-scaling systems, and are typically referred to as "competitive gamers" which is a far more neutral term. Though the term holds virtually the same meaning, as competitive gamers tend to focus entirely on a rule's usefulness on a tabletop and are (usually) disdainful of gimmicks or underpowered units.
A somewhat milder term with a similar meaning is "optimiser", which generally lacks the negative connotations of powergamer.
Munchkins
At the other end of the scale is the "twink" or "munchkin", which is almost always used to refer to someone who cares only about mechanical power (to the exclusion of roleplaying), or is willing to outright cheat if he thinks he won't get caught, or there will be no consequences if caught, as is demonstrated by the "Munchkin" series of card games by Steve Jackson Games.
Everyday powergamers are easily forgiveable, since there is a healthy respect for the way that any given game system functions, and their actions are perfectly excusable since the rules allow (and can be argued "encourage") them to do so. Depending on the setting or ruleset, a powergamer can garner a healthy measure of accolade for coming up with new levels of "optimal" play.
By contrast, Munchkins have a marked tendency to be more creative in their interpretations of rules; where a typical powergamer would look at a ruleset and use it to their maximum advantage, a munchkin's typical response to their detractors is that nothing in the rules say that they cannot do something.
In wargaming, the equivalent to munchkin would be WAAC (Win At All Cost) players, who focus almost entirely on overpowered/broken units or rules, rather than attempting to create an efficient or optimal army list.
True Munchkins rarely, if ever, gain positive recognition for their accomplishments.
Identifying a Powergamer
Powergamers are easy to spot based on their behaviour, which is generally the same regardless of which system/ruleset they are using.
In systems which undergo regular revisions or receive frequent updates, powergamers will often stand out due to their fickle attitudes. Often becoming obsessed with the next "new" rulebook/codex/splatbook which will either be an improvement over anything previously released or is new enough that it has not been effectively countered or debunked by the community at large. In these situations, a gamer who requests a re-roll of his character or sells his old army on ebay to fund his next one are generally going to be powergamers.
Lack of imagination when it comes to character/army builds is also a clear indication; people who hunt internet forums/help-sites for optimal builds tend to be powergamers, as it shows that the player is more interested in "winning" than actually playing the game in their own fashion. (see the rage summary below) Powergamers who also rely too heavily on public-domain builds can also reveal themselves to be poor players and tend to have the most difficulty adjusting when someone else presents them with a unique situation.
In Summary
If you've played against one in any game*, was it fun? Did you like having your balls ground to a pulp? Fuck no. Nothing is worse than that guy who spams Abaddon AND Kharn AND three fucking Land Raiders because of a technicality. They're all dedicated transports? FUCK THAT NOISE, GTFO MY STORE. Or they guy who manages to get 4 5 6 7 riptides in a single list because of GWs shitty wording that all have FNP.
Ever played against an IG armoured list. No? Pray you never do, because that list displays a level of asshattery (and disposable income) on a godlike level. Seriously, fucking TANKS as TROOP CHOICES?! OH FUCK THE FUCK OFF! Necrons don't care though so... Allies much?
For anyone playing a game simply to have fun and enjoy a good story, a powergamer is your number one enemy. Avoid at all costs. They'll fuck your shit up six ways to Sunday and five ways to Monday simply because they can.
*SenZar does not count.