What are the NIV cross-references? Where do they come from? In my NIV Bible I see tiny letters inside the text and references to other passages in the margins. Some of these are tremendously helpful, some seem only to relate by the use of one word. 

Where do these cross-references come from, did they originate with the authors of the NIV or are they from some older source? On what basis did the creators of this system decide that passage A should be related to passage B? Do we know the intention of the authors for how they should be used?
Before examining the New International Version use of cross-references, here is a brief look at the history behind Bible cross-references.


  “One of the fundamental principles of Protestant biblical interpretation is that "Scripture is its own best interpreter." Luther expressed this principle with the words, Scriptura sui ipsius interpres ("Scripture is its own expositor"), and it was summed up by the authors of the Westminster Confession thus: "The infallible rule of interpretation of Scripture is the Scripture itself: and therefore, when there is a question about the true and full sense of any Scripture ... it must be searched and known by other places that speak more clearly." For this reason the most important feature of any edition of the Bible (aside from the quality of the translation itself) is the system of cross-references provided in the margin, which helps the reader to find out the meaning of any hard place by "comparing spiritual things with spiritual" (1 Cor 2:13). A good set of cross-references, when used diligently and with intelligence, will make much commentary unnecessary.”  Source: http://www.bible-researcher.com/cross-references.html
  
  William Carpenter in the preface to his work Scientia Biblica from 1825 states: “The first collection of parallel passages the editor believes to have been that published with the third edition of Tyndale’s Testament, in 1534. Coverdale’s Bible, also, the first edition of which appeared in 1535, has a few marginal references. These were augmented and improved in the various editions of the Bible and New Testament, which were published subsequently to that time: the first edition of the present “Authorized Version” containing nine thousand references (Preface, p. vi)...  In 1683, the “Authorized Version” was corrected, and many additional parallel texts were added by Dr. Scattergood; and in 1690, Samuel Clark published “The Holy Bible, containing the Old Testament and the New, with Annotations and Parallel Scriptures,” &amp;c. In the Preface to this edition of the Scriptures, the Editor states that he took a great deal of pains in collecting parallel texts, and that not only for words and phrases, but for sense and matter.  Source: http://www.realbiblestudy.com/?p=91


From this, we can see how marginal notes and references can be traced back to 1534 and how, over time, they have been expanded.  With regard to how the NIV uses cross-references, we need look no further than the Introduction pages to the NIV Study Bible.  It has a cross-reference system of 100,000 entries.  The 1985 edition of the NIV Study Bible says this:


  “The cross-reference system, developed over many years by June Gunden, John R. Kohlenberger III (OT) and Donald H. Madvig (NT), can be used to explore concepts, as well as specific words.”


Pages xvi and xvii in my 2000 edition of the NIV Study Bible explain how the cross-reference system works.  Because this material is copyright, I am not at liberty to reproduce what it says, but I did find an on-line article which was published with the permission of Zondervan Publishing House. 

http://helpmewithbiblestudy.org/13reference/study_NIVStudyBible.aspx#sthash.YyZaZbiy.dpbs  

The intentions of the Committee on Bible Translation for the NIV Study Bible are explained in the Preface and your other questions about how cross-references should be used are explained in the Introduction pages.  I hope you find this helpful.