Rule 6.02(a): It is a balk when—

"With runners aboard and Angel Hernandez umpiring, it is a balk when"—so read the parody headline by a defensive team unhappy their pitcher was called for such an infraction, turning a potential out into a scoring position, run-producing opportunity. "Balkin' Bob Davidson" had previously been substituted in the umpires' line as had Joe West, though all MLB umpires have called multiple balks during their careers, except of course for Ron Luciano, who famously wrote: "I never called a balk in my life. I didn't understand the rule."
Trivia: A balk that ends a game may be referred to as a "balk-off." Also, Rex Hudler finds balks hilarious.
Quick Link: "Balk" coverage on the UEFL, including all balk-induced ejections since 2011.

Yet since Rule 6.02(a) [formerly known as Rule 8.05], which governs the balk, specifies 13 different criteria that may be satisfied for a balk to be called, the balk rule provides abundant material contributing to one of the most misunderstood segments of the baseball rules book:
The most common infractions have video links attached, illustrating each specific balk violation.

Definition: A balk is an illegal act by the pitcher as prescribed by Rule 6.02(a).
Eligibility: A balk may only be called when there is a runner or there are runners on base.
Penalty: Runners are given a one-base award unless more advantageous objectives are achieved.

(1) The pitcher, while touching his plate, makes any motion naturally associated with his pitch and fails to make such delivery (slips or trips [2] [3] / flinch / hesitation / shoulder turn / bad step / breaks motion [2] / fails to release / steps off during motion / start-stop / swings free foot past or behind rubber). This provision is symbolically first, for the balk is all about illegal deception. Provision (a) is the so-called all-inclusive provision, which outlines and provides a framework for the remaining 12 items under Rule 8.05.
(2) The pitcher, while touching his plate, feints a throw to 1st or 3rd base and fails to complete the throw. A fairly simple concept as far as balks go, with a runner on first (R1) or third (R3), a pitcher who motions to throw to 1st or 3rd base while on the rubber must complete the throw: The throw must get all the way to first base.
(3) The pitcher, while touching his plate, fails to step directly toward a base before throwing to that base. Also called the "no step balk," 8.05(c) requires the pitcher to step ahead of and in the direction of his throw (e.g., not toward home plate). This provision outlaws the third-to-first "wheel" move, unless, of course, the pitcher first breaks contact with the rubber.
(4) The pitcher, while touching his plate, throws, or feints a throw to an unoccupied base, except for the purpose of making a play. 8.05(d) authorizes the pitcher to throw to an unoccupied base for the purposes of catching a runner stealing, for instance, and prohibits the pitcher from faking a throw to an unoccupied base.
(5) The pitcher makes an illegal pitch. A quick pitch is one such illegal pitch associated with this rule. So is a pitch that never makes it to the foul line or plate or one thrown while not in contact with the rubber.
(6) The pitcher delivers the ball to the batter while he is not facing the batter. Hideo Nomo, for instance, was prohibited from releasing the ball while in his windup with his back turned to the batter.
(7) The pitcher makes any motion naturally associated with his pitch while he is not touching the pitcher's plate. In other words, the pitcher cannot fake a delivery while off the rubber.
(8) The pitcher unnecessarily delays the game. Interestingly enough, Rule 8.04 (12-second pitch timer) does not apply when runners are on base, while 8.05(h) does not apply when the pitcher is warned about delaying the game pursuant to Rule 8.02(c) (throwing to an unoccupied base when not attempting to make a play). Yet if a pitcher is ejected for delay of game, Rule 8.05(h) is also invoked.
(9) The pitcher, without having the ball, stands on or astride the pitcher's plate or while off the plate, he feints a pitch. Similar to Rule 8.05(g), the pitcher cannot fake a pitch. 8.05(i), however, covers the additional contingency of a pitcher pretending to pitch when he does not have the baseball.
(10) The pitcher, after coming to a legal pitching position, removes one hand from the ball other than in an actual pitch, or in throwing to a base. Once legally positioned or set, the pitcher must keep both hands (gloved and bare) together until he pitches, attempts a pick-off or other play or steps off the rubber.
(11) The pitcher, while touching his plate, accidentally or intentionally drops the ball. Self-explanatory.
(12) The pitcher, while giving an intentional base on balls, pitches when the catcher is not in the catcher's box. Known as a catcher's balk, this call is ordinarily made when: "it must be absolutely obvious."
(13) The pitcher delivers from Set Position without coming to a stop. This is very similar to 8.05(e), the quick pitch.

Myths
(2) A pitcher cannot fake a throw to first base. False; if the pitcher comes off the rubber, he becomes a fielder and enjoys all of a fielder's priveleges, including the ability to fake a throw to any base. In fact, stepping off the rubber relieves the pitcher of nearly all balk-related restrictions (except 8.05(g), etc.). Remember, a pitcher may disengage his plate for the purpose of this rule by stepping off with his pivot foot (or "back foot").
(3) The 45-degree line formed from the pitcher's plate to the midpoint between home plate and first base along the right field foul line governs 8.05(c). This is false, there is no angle designation in the Rules Book. Like a check swing, this makes 8.05(c) "ambiguous" (Ejection 027: Mike Muchlinski (1)).
(13) The pitcher must come to a stop or pause before attempting a pickoff. This is false; a stop is not required before a pickoff. A stop is only required out of Set Position before an actual pitch.
(-) The offensive team may "choose" whether to enforce a balk or take the result of a play. This is false; the resultant play is only upheld if runners have advanced at least one base and the batter has not been adversely impacted (e.g., by having been put out, etc.). The ball is live during a balk, and runners may advance beyond the base to which they are entitled at their own peril. Refer to the Balk Penalty.