The availability, feasibility and possible implementations of data protection depends on what we mean by the term. Protection from destruction isn't prohibitively difficult. Tiering on-line, near-line and off-line storage media with appropriate migration and duplication strategies is often sufficient to ensure the continued existence of one's information through all but the direst of disasters. Protecting data from unauthorized alteration isn't much more difficult since integrity and existence are positively correlated. That is to say, if information is corrupted or defaced having another copy allows one to roll-back at least. But complete protection from unauthorized access may be impossible even for those with immense resources (Das, 2008).
What one considers personal data might be an very exhaustive list. Medical history from birth to death, educational history, employment history, credit history, domiciles, marriages and other relationships and all of an individual's creations might be under the rubric; and some individuals may wish to keep some or even all of that private. I believe that is unrealistic. In the US HIPAA is an attempt to keep the medical data private (DoH, 2010), FERPA is an attempt at the educational (DoE, 2010) and various States have legislation that may protect some employment history (Epic, 2010). But one's credit history is for sale (Equifax, 2010), assembling a history of domiciles is a fairly trivial investigation, marriages are public records and other biographical facts can be easily ascertained if they were conducted in the public sphere. What the word public connotes and how deep and permanent the record is evolves as surveillance technology is accepted and deployed. From what I've seen I expect this is more or less the case globally. If one truly wants privacy one should probably stay away from urban and developed environments. Avoiding medicine, education, employment, banking (which could be easy with no employment), state sanctioned ceremonies and the publishing of one's work might also be beneficial.
Das, S. (2008) 'Quantum Cryptography Cracked?', IEEE Spectrum [Online]. Available from: http://spectrum.ieee.org/computing/it/quantum-cryptography-cracked (Accessed: 10 April, 2010)
Department of Education (2010) Family Educational Rights and Privacy Act [Online]. Available from: http://www2.ed.gov/policy/gen/guid/fpco/ferpa (Accessed: 10 April, 2010)
Department of Health and Human Services (2010) HIPAA [Online]. Available from: http://www.hhs.gov/ocr/hipaa/ (Accessed: 10 April, 2010)
Epic (2010) Workplace Privacy [Online]. Available from: http://epic.org/privacy/workplace/ (Accessed: 10 April, 2010)
Equifax (2010) Personal Solutions: Credit Reports, Credit Scores, Protection from Identity Theft [Online]. Available from: http://www.equifax.com/home/en_us (Accessed: 10 April, 2010)