The most important parameter to headphones (and speakers too) is frequency response - that is, how smoothly and perceptibly even the headphone reproduces the audible frequencies (20 Hz - 20 kHz). Everything else - driver material / type, headphone construction, etc. - can be considered 'window dressing'.
Currently, research relating frequency response to sound quality has produced the Harman Target curve. This is a frequency response for headphones that was obtained by measuring the response of sonically neutral speakers in a well-treated listening room using a head / torso simulator and further refined by listeners (trained and untrained) over a series of experiments. This would be your best shot at hearing a 'reference' or 'neutral' frequency response.
Several headphones follow the Harman curve - the AKG K371 ($149), the Mark Levinson No.5909 ($999) well as the Dan Clark Audio Stealth ($3999). Any of these headphones can be used as a reference. Importantly, there's little correlation between sound quality and price. For example, I've owned or listened to plenty of expensive headphones from the HD 800 to the Focal Utopia, STAX SR-009 and the DCA Stealth. The headphones I use daily are the AKG K371's. They sound very close to the Revel Ultima Studios I use in my stereo.
If you don't happen to like the sound of headphones tuned to the Harman curve, use an equalizer to find which frequencies need a boost or cut. Using your adjustments along with measurements of a headphone's frequency response can give you a better idea of which headphones would be better suited to your personal taste (if you don't feel like using an equalizer is a permanent solution). This frequency chart can help you in that process - EQ Cheatsheet.
Here's some more reading on the Harman curve in case you're interested:
Headphone Measurements Explained