Rule of thumb
A rule of thumb is a principle with broad application that is not intended to be strictly accurate or reliable for every situation.  It is an easily learned and easily applied procedure for approximately calculating or recalling some value, or for making some determination. Compare this to heuristic, a similar concept used in  mathematical discourse,  or in computer science, particularly in algorithm design. See also mnemonic.

# Examples of usage
Financial - Rule of 72
A rule of thumb for exponential growth at a constant rate. An approximation of the "doubling time" formula used in population growth, which says divide 70 by the percent growth rate (the actual number is 69.3147181 from the natural logarithm of 2, if the percent growth is much much less than 1%). In terms of money, it is frequently easier to use 72 (rather than 70) because it works better in the 4%-10% range where interest rates often lie. Therefore, divide 72 by the percent interest rate to determine the approximate amount of time to double your money in an investment. For example, at 8% interest, your money will double in approximately 9 years (72/8 = 9).
Tailors' Rule of Thumb
A simple approximation that was used by tailors to determine the wrist, neck, and waist circumferences of a person through one single measurement of the circumference of that person's thumb. The rule states, typically, that twice the circumference of a person's thumb is the circumference of their wrist, twice the circumference of the wrist is the circumference of the neck, and twice around the neck is the person's waist. For example, if the circumference of the thumb is 4 inches, then the wrist circumference is 8 inches, the neck is 16 and the waist is 32. An interesting consequence of this is that  for those to whom the rule applies  this simple method can be used to determine if trousers will fit: the trousers are wrapped around the neck, and if the two ends barely touch, then they will fit. Any overlap or lack thereof corresponds to the trousers being too loose or tight, respectively.
Marine Navigation
A ship's captain should navigate to keep the ship more than a thumb's width from the shore, as shown on the nautical chart being used. Thus, with a coarse scale chart, that provides few details of nearshore hazards such as rocks, a thumb's width would represent a great distance, and the ship would be steered far from shore; whereas on a fine scale chart, in which more detail is provided, a ship could be brought closer to shore.
Statistics
The Statistical Rule of Thumb says that for most large data sets, 68% of data points will occur within one standard deviation from the mean, and 95% will occur within two standard deviations. Chebyshev's inequality is a more general rule along these same lines and applies to all data sets.
Hazardous Material Emergency Response
Hazardous material (hazmat) emergency responders in the US are trained to various levels of capability for action during a hazmat incident, with names for the capabilities varying by locale.  Typically, basic-level responders are trained to be able to recognize various types of hazardous materials and establish an isolation perimeter around the site of the incident.  Basic-level responders will observe the "Rule of Thumb" for establishing a minimum safe distance from a hazmat site.  If the responder is uphill and upwind from the incident, and they are able to visually cover the site with a thumb held at arm's length, they are assumed to be a safe distance away from the event.  Of course, this varies greatly depending on the nature of the hazmat incident, and should only be used as a general guideline.  More specific information about hazardous material isolation is available in a material's material safety data sheet, or in such documents as the Emergency Response Guidebook, published by Chemtrec in the US.  Other countries typically have their own hazmat emergency response resources.
Etiquette
In a formal place setting, the silverware and the dinner plate should be set back from the edge of the table a length equal to the distal phalanx of the thumb.

# Origin of the Phrase
The earliest citation comes from Sir William Hopes The Compleat Fencing-Master, second edition, 1692, page 157: "What he doth, he doth by rule of thumb, and not by art"
The notion that the "rule of thumb" was a law that limited the width of a rod that a man may use to beat his wife has been partially discredited.  Wife beating has been explicitly illegal in British law since the 1700s, and has never been legally sanctioned in America. However, at least four judges and other legal authorities from 1782 to 1897 have referred to the bogus law in spite of the fact that it never existed.The non-law gained popularity after feminist Del Martin wrote in 1976:
Our law, based upon the old English common-law doctrines, explicitly permitted wife-beating for correctional purposes. However . . . the common-law doctrine had been modified to allow the husband 'the right to whip his wife, provided that he used a switch no bigger than his thumb'--a rule of thumb, so to speak.
It is now firmly entrenched as an urban myth.