Which approach category minimums should I use when conducting an instrument approach? FAR 91.3 says:


  Aircraft approach category means a grouping of aircraft based on a
  speed of VREF, if specified, or if VREF is not specified, 1.3 Vso at
  the maximum certificated landing weight. VREF, Vso, and the maximum
  certificated landing weight are those values as established for the
  aircraft by the certification authority of the country of registry.
  The categories are as follows—
  
  (1) Category A: Speed less than 91 knots.
  
  (2) Category B: Speed 91 knots or more but less than 121 knots.
  
  (3) Category C: Speed 121 knots or more but less than 141 knots.
  
  (4) Category D: Speed 141 knots or more but less than 166 knots.
  
  (5) Category E: Speed 166 knots or more.


So an aircraft category never changes because it is always Vref at max landing weight.  

What if I fly an approach at a speed that falls into a different category?  For instance, a jet may land at significantly less than this speed if very light, or more than this speed if landing with less than full flaps due to a failure (or any other operational reason).  Which minimums do you use then?
According to the FAA Safety Alert for Operators issued on 09/20/2012 (SAFO 12005):


A pilot may never use the approach minimums specified for an approach category lower than their certified approach category, even if the actual approach is flown at a speed that would be in the lower approach category.
A pilot must always use the approach minimums specified for an approach category higher than their certified approach category if the actual approach will be flown at a speed that would be in the higher approach category. 


Note that this is different in other areas of the world (Canada for example uses the actual approach speed of the aircraft to determine the approach category).