Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 adj. Conforming with, adhering to, or constituting a norm, standard, pattern, level, or type; typical: normal room temperature; one's normal weight; normal diplomatic relations.
 adj. Biology Functioning or occurring in a natural way; lacking observable abnormalities or deficiencies.
 adj. Chemistry Designating a solution having one gram equivalent weight of solute per liter of solution.
 adj. Chemistry Designating an aliphatic hydrocarbon having a straight and unbranched chain of carbon atoms.
 adj. Mathematics Being at right angles; perpendicular.
 adj. Mathematics Perpendicular to the direction of a tangent line to a curve or a tangent plane to a surface.
 adj. Relating to or characterized by average intelligence or development.
 adj. Free from mental illness; sane.
 n. Something normal; the standard: scored close to the normal.
 n. The usual or expected state, form, amount, or degree.
 n. Correspondence to a norm.
 n. An average.
 n. Mathematics A perpendicular, especially a perpendicular to a line tangent to a plane curve or to a plane tangent to a space curve.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. According to norms or rules.
 adj. Usual; ordinary
 adj. Healthy; not sick or ill
 adj. Pertaining to a school to teach teachers how to teach.
 adj. of, relating to, or being a solution containing one equivalent weight of solute per litre of solution.
 adj. Describing a straight chain isomer of an aliphatic hydrocarbon, or an aliphatic compound in which a substituent is in the 1 position of such a hydrocarbon
 adj. (Of a mode in an oscillating system) In which all parts of an object vibrate at the same frequency; See normal mode
 adj. Perpendicular to a tangent line or derivative of a surface in Euclidean space.
 adj. (Of a subgroup) whose cosets form a group
 adj. (Of a field extension of a field K) which is the splitting field of a family of polynomials in K
 adj. (Of a distribution) which has a very specific bell curve shape
 adj. (Of a family of continuous functions) which is precompact
 adj. (Of a function from the ordinals to the ordinals) which is strictly monotonically increasing and continuous with respect to the order topology
 adj. (Of a matrix) which commutes with its conjugate transpose
 adj. (Of a Hilbert space operator) which commutes with its adjoint
 adj. (Of an epimorphism) which is the cokernel of some morphism
 adj. (Of a monomorphism) which is the kernel of some morphism
 adj. (Of a morphism) which is a normal epimorphism or a normal monomorphism
 adj. (Of a category) in which every monomorphism is normal
 adj. whose digits, in any base representation, enjoy a uniform distribution
 adj. (Of a topology) in which disjoint closed sets can be separated by disjoint neighborhoods
 adj. in the default position, set for the most frequently used route.
 n. A line or vector that is perpendicular to another line, surface, or plane.
 n. A person who is normal, who fits into mainstream society, as opposed to those who live alternative lifestyles.
from the GNU version of the Collaborative International Dictionary of English
 adj. According to an established norm, rule, or principle; conformed to a type, standard, or regular form; performing the proper functions; not abnormal; regular; natural; analogical.
 adj. According to a square or rule; perpendicular; forming a right angle. Specifically: Of or pertaining to a normal.
 adj. Standard; original; exact; typical.
 adj. Denoting a solution of such strength that every cubic centimeter contains the same number of milligrams of the element in question as the number of its molecular weight.
 adj. Denoting certain hypothetical compounds, as acids from which the real acids are obtained by dehydration; thus, normal sulphuric acid and normal nitric acid are respectively S(OH)6, and N(OH)5.
 adj. Denoting that series of hydrocarbons in which no carbon atom is bound to more than two other carbon atoms; Cf. Iso.
 n. Any perpendicular.
 n. A straight line or plane drawn from any point of a curve or surface so as to be perpendicular to the curve or surface at that point.
from The Century Dictionary and Cyclopedia
 According to a rule, principle, or norm; conforming to established law, order, habit, or usage; conforming with a certain type or standard; not abnormal; regular; natural.
 Serving to fix a standard; intended to set the standard: as, a normal school (see below).
 In music, standard or typical: as, normal pitch or tone, a pitch or tone of absolute acoustical value, which is used as a standard of comparison. See key, 7, and natural key (under key).
 In geometry, perpendicular: noting the position of a straight line drawn at right angles to the tangentline of a curve, or to the tangentplane of a surface, at the point of contact.
 Synonyms Regular, Ordinary, Normal. That which is regular conforms to rule or habit, and is opposed to that which is irregular, fitful, or exceptional. That which is ordinary is of the usual sort and excites no surprise; it is opposed to the uncommon or the extraordinary. That which is normal conforms or may be figuratively viewed as conforming to nature or the principles of its own constitution: as, the normal action of the heart; the normal operation of social influences; the normal state of the market.
 n. In geometry, a perpendicular; the straight line drawn from any point in a curve in its plane at right angles to the tangent at that point; or the straight line drawn from any point in a surface at right angles to the tangentplane at that point. See cut under binomial.
 In chem.:
 Of a salt, having all the readily replaceable or basic hydrogen of the corresponding acid replaced by one or more metals or strongly electropositive radicals: distinguished from an acid salt in which this replacement is only partial.
 Of a solution for use in volumetric analysis, containing of the dissolved chemical substance the reactive equivalent of 1 gram of hydrogen in 1 liter of the solution at 16° C. See normal solution.
 n. The rule; the standard.
 n. In biology, a species or race considered as a fixed standard which individual organisms may approach by heredity and from which they may recede by variation.
 n. In meteorology, the average of a large number of observed values of any given meteorological element, for example, mean temperature, pressure, or rainfall for any hour of the day, or day of the year. The number of observations must be so large that a second group of the same number would give the same average or normal. The normals for the hours of local mean solar time may be corrected or adjusted so as to become normals for the hours of any other standard of time.
 n. In compar. psychol., an untrained or uninjured animal whose behavior is made the standard of reference for the interpretation of the conduct of other, trained or operated animals.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 adj. forming a right angle
 adj. conforming with or constituting a norm or standard or level or type or social norm; not abnormal
 adj. being approximately average or within certain limits in e.g. intelligence and development
 adj. in accordance with scientific laws
 n. something regarded as a normative example
Etymologies
from The American Heritage® Dictionary of the English Language, 4th Edition
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

If the response is that it is used, but not with its normal semantic value, then we are left with the challenge of defining ˜normal™ and ˜abnormal™ semantic values.

predominantly a normal existence ... which continued to be a normal existence, not only at the will or whim of this antisocial pathological mental condition.

I was starting to realize that the term normal was relative.

People who understand, like Dr. Stewart, that the word normal is inclusive.

But the word normal was never used to describe me.

Salatin's use of the term "normal" is crucially important when discussing local and sustainable foods.

The term normal…refers to class culture that is not lower class.

What with being abandoned by my mother as an infant and growing up in a twohundredyearold farmhouse in the middle of 148 acres with a nut cake father bless his heart and no neighbors in sight, no relatives, no friends, no TV—the word normal would not apply to any other aspects of my personality.

But, it turns out that the NWS is also using the term normal in addition to average and also mean.

I fear that some of our discussions about human sexuality thus far have confused the term "natural" with the term "normal."
anydelirium commented on the word normal
'I have no confidence in the normal, wellbalanced type of persons.' The Fall of the House of Usher, by Edgar Allen Poe
February 19, 2008