Since there are two points from two posters that contain the same question let me answer this question and then I'll reply specifically to other germane points.
Okay, well unfortunately you all have asked me a question that I've actually done some research on during my PhD coursework...so....
The issue of the orientation of King James I (VI if you're Scottish) is almost without question in contemporary historical scholarship. Given that we possess the originals of his romantic correspondence between three male lovers the point is without question. The evidence is overwhelming that James had romantic (and frankly sexual) relationships with at least three men: Esmé Stuart, Robert Carr, and George Villiers. If you take time to read the letters you'll want to repent of his sin for him soon after.
I'll refer you to the text
King James' Letters of Homoerotic Desire edited by David Beregon
http://www.amazon.com/dp/0877456690/?tag=baptis04-20
Anyone consulting several of his recent biographies will find discussion of this attraction in James' life. Please refer to the following:
Great Britain's Solomon : James VI and I in His Three Kingdoms by Martin Lee
http://www.amazon.com/dp/0252016866/?tag=baptis04-20
Majestie: The King Behind the King James Bible by David Teems
http://www.amazon.com/dp/B0058M5GMW/?tag=baptis04-20
An additional textual resource is a sexual history of James I's life:
Royal Family, Royal Lovers: King James of England and Scotland by Beregon
http://www.amazon.com/dp/0826207839/?tag=baptis04-20
and
King James & the History of Homosexuality by Michael B Young
http://books.google.com/books?id=7hmKQgAACAAJ&hl=en
Frankly, there are other works out there and any number of histories of England of this time will discuss the reality of this fact. Also, a number of recent biographies of the King James Bible produced to honor its 400th Anniversary do recognize the orientation of James.
You can go and look up these resources yourself if you choose. Quite simply the issue is as certain a historical reality as we have. To bring this to somewhat a close I point to a text from Justo Gonzalez's
The Story of Christianity vol 2 which is the standard Christian history textbook for most evangelical seminary classes. In his description of James I, Gonzalez writes this:
Jame's personal character did little to increase his prestige. He was a homosexual, and his favorites enjoyed unmerited privileges and power in his court and in his government. While insisting on his right to an absolute monarch, he wavered between stubborn rigidity and weak flexibility. (pg 152)
I leave you with this evidence. As a final point I simply link to the Wikipedia entry for anyone still unbelieving:
http://en.wikipedia.org/wiki/Personal_relationships_of_James_VI_and_I
It has links to other works.