Do Mormons respect the EU "Data Protection Directive" of right of access to personal data? For some background: the EU "Data Protection Directive" is a European Union directive which regulates the processing of personal data within the European Union, as explained in this Wikipedia article. Among these regulations is the rule that individuals have right for a copy of the data that has been collected about them.

About this the document A European Perspective on Data Protection and Access Rights says (on. p. 6):


  Hence, although with a veiled expression, Art. 12 entitles the data
  subject to exercise the following four rights:
  
  
  the right to confirmation as to whether or not data relating to the data subject are being processed by a particular controller and, if
  so, to obtain details of the processing (Art. 12 (a), first indent);
  the right of access to one’s data, including the right to have a copy of the data in question with any available information as to
  their source (Art. 12 (a), second indent);
  the right to have the data rectified, erased or blocked if they do not conform to the Directive, in particular if they are incomplete or
  inaccurate (Art. 12 (b));
  the right to be informed about the logic used in case of automated decisions (Art. 12 (a), third indent).
  


Similar sentiments have been expressed in other documents, such as the "Charter of Fundamental Rights of The European Union", p.10:



So on this note, I was browsing Wikileaks earlier today and noticed an image listed on a page titled "LDS Church exclusion of members access to their own records 2008" (This page is under the Category:The Church of Jesus Christ of Latter-day Saints).

The image, shown below, shows a screen shot of a dialog from software application. The text on the dialog starts with "Members may not have copies of their membership records. Under no circumstances may membership records be given to anyone other than the bishop or a clerk."



The question I wanted to ask is, how does the LDS church handle requests for copies of personal data that come from EU?
I know that software first-hand because I served as a ward clerk.

The quote is misleading. On the "members record" appears information about parents, children and husband/wife, along with their member number.

Members may have access to a so-called "summary of ordinances" (translation from german, i don't know the english  name). The only difference is that the member number of other persons (parents  etc.) do not appear. Clerks are encouraged to regularly show that summary to the member to check correctness, and members can keep it if they want.

The member number is identifying information that is used, for example, to register an account on lds.org. Giving that number to someone else would be the actual data protection issue.

I am aware this may only partially answer your question, but maybe it clears up some confusion.