What are the criteria for "variable" in METAR reports?
There are two official sources to take into account:


ICAO Annex 3 to the Chicago Convention is the reference for meteorological information. Annex 3 applies to all ICAO members (countries), unless stated otherwise.
Members departing from ICAO recommendations state differences in their country AIP, section GEN 1.7.


ICAO Annex 3

§ 4.1.5.2:


  1) when the total variation is 60° or more and less than 180° and the
  wind speed is 6 km/h (3 kt) or more, such directional variations shall
  be reported as the two extreme directions between which the surface
  wind has varied
  
  2) when the total variation is 60° or more and less than 180°
  and the wind speed is less than 6 km/h (3 kt), the wind direction
  shall be reported as variable with no mean wind direction; or  
  
  3) when the total variation is 180° or more, the wind direction shall be
  reported as variable with no mean wind direction"


So for ICAO there are three cases:


The wind is significant (more than 6 km/h) and there is a predominant direction (varying by less than 60°), possibly with some gusts: the three data are reported in the form 31015G27KT.
There is a significant wind (more than 6 km/h) but the direction varies a lot (between 60° and 180°): Mean direction, speed and gust are reported in the same form, and direction range is reported using V, e.g. 31015G27KT 280V350.
There is no clear wind direction, either because the speed is low (less than 6 km/h) or the direction varies by more than 180°: No direction is reported, only a speed with the indication VRB is used, e.g. VRB02KT.


Country AIP

US AIP:


  The wind direction may be considered variable if, during the 2-min
  evaluation period, the wind speed is 6 KT or less. Also, the wind
  direction shall be considered variable if, during the 2-min evaluation
  period, it varies by 60 deg or more when the wind speed is greater
  than 6 KT.
  
  Practices define wind gusts as rapid fluctuations in wind
  speed with a variation of 10 knots or more between peaks and lulls. 
  Wind speed data for the most recent 10 minutes is examined and a gust,
  the maximum instantaneous wind speed during that 10-minute period, is
  reported if the definition above is met during that period.


ATC instructions given in PANS ATM Doc 4444, § 12.3.1.7a are also refined:


  In the U.S., the criterion for a variable wind is: wind speed greater
  than 6 kt and direction varies by 60 degrees or more. If the wind is >1
  kt but &lt;6 kt, the wind direction may be replaced by ”VRB” followed by
  the speed or reported as observed. “VRB” would be spoken as “wind
  variable at .”


In the US, VRB indication is slightly different than in ICAO recommendations: VRB can be used regardless of the direction variation, when the wind is less than 6 kt (not 6 km/h) or if the variation is more than 60°. This covers the last two cases of ICAO.




METAR panel at Weeze tower (EDLV). source: Airplane Pictures, photo by Zonan Adolfse