The Rules.

FAR 91.411 and FAR 91.413  

 "91.411 states that you may not operate an airplane or helicopter in controlled airspace under IFR unless you have had your static pressure system, altimeter and automatic pressure altitude reporting system tested in the preceding 24 calendar months." 

Its pretty cut and dried - if you want to operate in controlled airspace, you will have to have the IFR certification done. By the same logic, if you don't want to operate in controlled airspace - then you don't need it. 

"91.413 states that no person may use an ATC transponder unless it has been tested in the preceding 24 months." 

This one has no options attached to it - if you've got one installed, it has to be tested.

 Appendix E of part 43 describes the Altimeter System Test and Inspection (91.411) requirements. 

• Static Pressure system - Is inspected to ensure that it is free from restrictions and trapped moisture, that any heater installed is operative, that there are no alterations or deformations to the airframe. The system then has to be leak tested to a given set of tolerances. 

• Altimeter - Has to be tested for Scale Error, Hysteresis, After Effect, Friction, Case Leak and Barometric Scale Error

• Automatic Pressure Altitude Reporting Equipment and ATC Transponder Integration Test - Has to be tested to measure the automatic pressure altitude replies on Mode C  and at enough test points to ensure the system is functioning as intended and that the difference between the reporting and displayed altitude is less than 125 ft.