It seems confusing to have so many translations of the Bible. Why isn't there just a single (English) one? Or maybe a single "modern" one (given that KJV is hard to understand these days).
Being a speaker of a minority language, I can state one good reason and many -- well, not so good ones.
The good reason
Language changes. In some languages, you only have different Bible translations for this reason: the translations are temporally spaced maybe a hundred years apart.
Look at 2 Timothy 2:15 in different English translations:
It's quite necessary to renew the Bible translation time to time, so that people can understand it. The 1769 KJV is still quite understandable for the most part, but the reasons are cultural. The huge popularity of the KJV has kept its language alive.
The not-so-good reasons
There are other reasons, which vary from good to bad in different instances. First, there are the different translation philosophies already discussed in another question -- this amounts to multiple reasons. Note that there are benefits to having different types of translations.
Then there are the doctrinal reasons -- in my opinion, bad reasons. I'll show just one example, the New World Translation's take on John 8:58.
Looking at other English translations of John 8:58, every one of them translates the end as "I am." Looking at an interlinear version, one can be quite sure that the NWT translates the passage on a purely doctrinal basis.
What's very interesting is that the Watchtower Society has an interlinear of their own, and even that translates the phrase as "I am" while also showing the NWT "I have been":
The bad reason turned good reason
If the NWT was the only available translation in English, it would almost force a new translation to be made. Take a bunch of errors such as the one shown above, and the translation gets too unreliable.
Of course, the errors need not be especially crafted to suit some doctrine; they can be made of ignorance, disbelief in the original, etc. First translations in a new language (e.g. what the Wycliffe Bible Translators are doing) almost necessarily contain errors, as many needed terms are very hard to find for a non-native speaker. Whatever the reasons are, a large amount of errors is a good reason to create a new translation.
English Bible Translations differ for a number of reasons:
1. Differences in the English language. Dancek's excellent answer points out how the English language changes over time. In addition, some translations are more dialect-specific (American English vs British English).
2. Sources used for the translation
Bible translators use a wide variety of source materials, including but not limited to:
Many modern scholars think the Alexandrian manuscripts used to make up the "critical text" are earlier and more reliable. Other scholars strongly disagree, preferring the "majority text" for a variety of reasons.
Some modern translations use a single source, others try to harmonize multiple sources. Many modern English versions are based primarily on other prior versions. Plenty of examples here.
3. Different stated purposes for creating the translation. A few examples:
4. Translation philosophy (Dynamic vs Formal Equivalence).
This is easiest to illustrate using an example: how would you translate the following Spanish phrase:
A very literal word-for-word translation (formal equivalence) might be "What do you call yourself?" or perhaps "What are you called?". This is understandable, but is a little awkward in English.
A modern English speaker would probably ask this question as "What is your name?" This would be an example of dynamic equivalence, which translates idea-by-idea instead of word-by-word.
Translations are only approximations of the original text. Each translation of the Bible will vary on two levels: (1) The scholar's study and understanding of specific phrases and what they mean, and (2) the purpose of the translation which can vary from a staunch adherence to the original phraseology to freely changing the text for the purpose of increasing mainstream understanding and clarity.
When you translate a work from times of antiquity, you have to make some tough choices between translating the original words (literal translation) and preserving the meaning and intention of the original work for the modern ear.
A "chair" in ancient Greek or Hebrew or Aramaic is largely a chair in modern English; Easy enough. But what about phrases and idioms that do not have a direct translation? Sometimes even entire concepts and traditions don't even exist in modern languages. How do you translate those?
For example — In ancient Egypt, wielding a name held great power. If you curried favor with a god (for example), it was believed that you could evoke their name and have them do your bidding at will. That practice was an abomination to the Hebrews and their teachings in that God's name was to be treated with utmost reverence and never evoked for such trivialities like mere mortal endeavors. So when the Hebrews read the original text of the Third Commandment "taking of the Lord's name in vain," they new exactly what was being prohibited. Today, the concept is largely lost so there isn't even a colloquial phrase to describe the prohibition. So we're left with a bit of ambiguity in the text of the Third Commandment which is interpreted to mean anything from "don't say 'bad' words" to "you do NOT tell God what to do, He tells you what to do!"
The same goes for the various nuances of what a passage means by "love," or conveying the meaning of "to kill" vs. murder vs. slaughter. Even a single mention of the word "manger" evokes portrayals of Mary and Joseph traipsing out into the field to to stay in the little red building out back. So decisions are made to faithfully translate the words as written, or rewriting the passage to closer approximate the original meaning of the text. Tough choices.
Two more reasons:
I think that dancek and warren covered the good reasons for the different versions: language changes. Also the not-so-good reasons: philosophies.
One other reason that I think has come about recently is publisher fees. The big houses like Lifeway and Crossway can save money on their products if they do not have to pay fees for the NIV and NASB translations. From this you get ESV and HCSB. You will see many of the Lifeway resources using the HCSB now.
Some translations are created so they can be free like the New English Translation (NET)
Referencing the wikipedia article:
The main reason that multiple versions exist, in my opinion, is that when you translate from one language into another, you have to make choices and decisions as to the methods employed. Consider the translations of Homer, Beowulf, Sun Tzu, and countless others - are the English versions identical to the originals? No. Are they as close as can be reasonably made? Yes.
With the different translation philosophies in use (dynamic equivalence, formal equivalence (similar to literal translation), and idiomatic or paraphrastic translation), you are bound to get multiple "versions".
Other linguistic issues arise when there are multiple words that can be translated (properly) for a given original, or when there are multiple originals that can only be translated into one word (eg the Greek words for love - agape, philia, eros, storge : they are all translated "love" in English because we [tend to] prefer one word with multiple definitions over multiple words each with one definition).