Score Multiplier

Something that rewards more points in Video Games. Ways of obtaining them may include:

Collecting and/or using special items
Cheats
Initiate an event
Kill Streak

Examples of Score Multiplier include:

Board Games

The double/triple letter/word squares in Scrabble.

Video Games

In most Super Mario Bros.. games, your score is multiplied by a Kill Streak. You eventually get 1-Ups instead when the streak is high enough.
In Wet, the score multiplier is automatically ramped up by killing enemies really fast. However, in boss battles, there are also one-time-only score multipliers that can be picked up (usually through acrobatic jumps) and stack with the regular multipliers.
Nearly all Falling Blocks puzzle games have the multipliers. They're all based around doing a rapid succession of matches or making a match that causes other matches to appear. Panel de Pon is the one most reliant on this, as the game moves at a relentless pace and requires such chains both to keep up and to keep the opponent at bay.
Bejeweled Blitz includes multipliers that you can score.
The Ratchet and Clank games have done this since the second game. The New Game+ mode gives a bolt multiplier that lasts until Ratchet takes damage.
Lego Crossover Games with their stud multipliers.
Crystal Caves
Guitar Hero
Tony Hawks Pro Skater, Tony Hawk's Underground and Gun all use some variant upon this (all were designed by Neversoft).
The different kinds of execution in Manhunt arguably qualify.
Grand Theft Auto II: you often receive a fixed amount of points (which equal money), but it is then multiplied by a number you can increase by completing missions, and picking up some power-ups.
In Gears of War 3, you can play an "Arcade" version of the campaign where your score in recorded in which enemies you kill. So many points reaches another multiplier level where you get more points for each kill and the multiplier goes down when a player character goes down, if a player is killed the score resets to X1.
Some of the activities in Saints Row, such as Mayhem and Insurance Fraud, require you to gain these in order to succeed.
Fisher-Diver has gems which give a score increase. The multiplier resets when returning to the surface.
In Lady Bug, eating blue hearts can increase the score multiplier, which goes from 2x to 3x to 5x.
Giga Wing gives out tokens that increase your score the more you grab.
Kingdom Hearts Re:coded had an option for increasing the rate of spell experience at the cost of reduced level experience.
Final Fantasy VI has the experience egg, which doubles XP earned.
Final Fantasy XII has an item that doubles license points earned, and another item that doubles XP earned.
The Bit.Trip series games give these for sustained combos, which is required to form a top or high score.
Blitter Boy has a score multiplier that slowly increases as you pick up more and more money. As there's nothing stopping you from dragging the first level out perpetually, this can used to gain an unreasonably large multiplier before continuing onto the later levels.
Geometry Wars has a multiplier that increases the longer you stay alive. Considering your score earns you both additional bombs and lives, using the former is instrumental in keeping the multiplier going, and thus earning more of both.

Web Games

Boxhead: The Zombie Wars: the more zombies you kill in a given length of time, the higher your point multiplier becomes.

Real Life

Some Lotto and Powerball games have "multipliers." If you pay an extra $1 your hypothetical winnings are increased by a multiple of 2, 3, etc. if that's what they pick for that night.