Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 n. A quantity, such as mass, length, or speed, that is completely specified by its magnitude and has no direction.
 n. Mathematics A number, numerical quantity, or element in a field.
 n. A device that yields an output equal to the input multiplied by a constant, as in a linear amplifier.
 adj. Of or relating to a scalar.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. Having magnitude but not direction
 adj. Of, or relating to scale
 n. A quantity that has magnitude but not direction; compare vector
 n. An amplifier whose output is a constant multiple of its input
from the GNU version of the Collaborative International Dictionary of English
 n. In the quaternion analysis, a quantity that has magnitude, but not direction;  distinguished from a vector, which has both magnitude and direction.
from The Century Dictionary and Cyclopedia
 n. In quaternions, a real number, positive or negative, integral, fractional, or surd: but some writers lately extend the meaning so as to include imaginaries.
 Of the nature of a scalar.
 n. In physics, a quantity, such as mass or volume, which has magnitude but not direction.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 adj. of or relating to a directionless magnitude (such as mass or speed etc.) that is completely specified by its magnitude
 adj. of or relating to a musical scale
 n. a variable quantity that cannot be resolved into components
Etymologies
Examples

The cult leader warns that her followers will make and defend themselves with what she calls scalar electromagnetic weapons if they are attacked, just as Aum defended itself when it was threatened.

The triple product is sometimes called the scalar triple product to distinguish it from the vector triple product

This is related to Grice's first maxim of quantity ( "Make your contribution as informative as required") and is held responsible for the inference of socalled scalar implicatures, among others.

Mass, electric charge, temperature, have the same symmetry, of a type called scalar, that of the sphere.

Electromagnetic waves which exist only in the vacuum of empty space constitute an ocean of infinite energy called scalar energy.

If you remember your math (and even if you don't), a scalar is a plain, simple, onedimensional value.

In Perl, a scalar is the fundamental, basic unit of data of which there are two kindsnumbers and strings.

Arithmetic types, enumeration types, pointer types, and pointer to member types are collectively called scalar types.

Jcoupling, also known as scalar coupling, is due to the interaction between different nuclei in the same molecule that is mediated through electrons in chemical bonds

Scalar Subqueries in SQLA subquery that returns exactly one column value from one row is also referred to as a scalar subquery.
Wordnik is becoming a notforprofit! Read our announcement here.
ruzuzu commented on the word scalar
(BTW, check out the clouds showing KelvinHelmholtz instability in the visuals.)
August 29, 2011
ruzuzu commented on the word scalar
"2. In quaternions, a real number, positive or negative, integral, fractional, or surd: but some writers lately extend the meaning so as to include imaginaries. Sir W. R. Hamilton introduced the word with the meaning “a real number”; and it tends to confuse the subject to use a word needed for one purpose to signify something else for which no new word is needed."  Cent. Dict.
August 29, 2011