Who was King James, and is there any evidence that he edited the Bible to meet his own beliefs?

Up until the early 17th century, there was no "official" version of the Bible in English. Various translations, such as the Geneva and Great Bibles were available, but they tended to reflect the prejudices of their authors in the way they translated from the original.

King James had been King James VI of Scotland since 1567, and when the thrones merged in 1603, on the childless death of Elizabeth I, became King James I of England, and he ruled England, Scotland and Ireland until his death in 1625. He was a literary man, writing a number of works, perhaps most notably 'A Counterblast to Tobacco', one of the first anti-smoking works.

In 1604, he called a conference at Hampton Court Palace, and proposed a new translation of the Bible, to replace the existing versions in popular use. There's no evidence he edited the Bible himself, but he did provide the translators with guidelines for their work. They may be seen here:
http://www.av1611.org/kjv/kjvhist.html

The translation was carried out by 54 scholars in six committees, who worked on separate sections. The scholars were not paid for their efforts, which took seven years to complete, with the first edition being published in 1611. Because of its special status, while it is now public domain and may be freely reproduced elsewhere in the world, it remains under copyright in the United Kingdom.

My own personal favorite here is where it appears that the translators working for King James failed to actually translate some words into English since such literal translation would conflict with church doctrine.

An example is the word "baptism". The word "baptizo" in Greek is literally translated "dip", "plunge", or "immerse". Since the Church of England sprinkles, it was necessary to transliterate the word and create a new word "baptize" to keep the meaning vague to English readers.

Churches have suffered from this interesting decision ever since.

Another example as requested: 1 Timothy 3:11 - KJV translates this passage as "Even so must their wives be grave, not slanderers, sober, faithful in all things"

This passage is discussing the qualifications of deacons/servants/ministers of the church. The implication in the King James is that verse 11 is discussing their wives. However, the word "their" is not in the Greek. The Greek word "gune" can mean "wife" or "woman". However, the KJV translators inserted this possessive pronoun seemingly to not allow for the possibility that some deacons (like Phoebe in Romans 16) could be women. Without the pronoun, this passage takes on a little different meaning (see NASB, ESV, NIV, ASV, etc... for a more accurate translation). Of course verse 12 discusses deacons being husbands of one wife, so this must be dealt with as well in terms of the gender question. However, verse 11 cannot be used to make the argument.

It's also interesting to note that the word "deacon" in this chapter of 1 Timothy is not an English word but another transliteration. This has caused many problems in churches that have turned this position of "special servant" into a church office akin to that of a "junior elder". Deacons/servants were a distinct group performing tasks assigned them by elders (and had to have certain character traits, per this passage), but this hierarchical structure is not supported in scripture. The transliteration supports church hierarchy that is popular among many orthodox religions (including the Church of England of this time) but is contrary to the way the New Testament writers describe "diakonos" throughout scripture.

king james did not have a good reason for another translation. king james authorized another translation because he did not like the geneva bibles notes, like exodus 1:17 note that said the hebrew midwives were right to disobey the egyptian kings command to kill all the male babies. king james did not want anyone to disobey him. the puritians and pilgrims used the geneva bible and did not join the church of england. king james did not like them. after the king james bible was printed in 1611 king james made ownership of the geneva bible a felony. the geneva bible was translated from original hebrew and greek. i do not believe the king james version is a bad translation. genevabible.com and tolle lege press has geneva bibles.

There is one interesting point not of King James' editing, but more of a tribute. It was pointed out to me by a native German speaker who got completely bewildered the first time he heard an English speaker mention the Book of James. His German Bible has no such book. He found that this is the Book of Jacobe (with the J given the Y pronunciation per German). Upon investigation, he learned, and I confirmed, that whenever the translators encountered the Hebrew word for the patriarch Jacob, even in the New Testament, they translated it Jacob. Whenever they encountered the Greek form of that name, they translated it James. So at least there was a method to the madness.

While I don't believe King James originated the idea of transliterating "baptizo" rather than translate it dip, or of translating the word "ekklesia" (assembly) as "church", his translation certainly perpetuated the obscuring of the impact and implications of those words, under which the State Church or High Church don't fare so well. Note rule number 3 in the KJV history mentioned in another answer:
http://www.av1611.org/kjv/kjvhist.html