Choosing a version of the Bible is hard, and to tell the truth I haven't done a great deal of research. I've read what various scholars have said about the versions, but I'm not linguistically qualified to judge the translations based on their own merits -- if I were, I wouldn't need a translation, I could just read the Bible in the original languages! The main reasons I chose the NIV are:
1. The NIV is based on more (quantity) and more recent manuscripts than just about any other version.
2. It was translated independently by several teams who then compared their results to ensure accuracy.
3. I find it very readable.
4. It appears to accurately translate the thoughts of the original texts into the appropriate English words. That is, it is a "thought-for-thought" (TFT) translation rather than "word-for-word" (WFW). The main problem I have with WFW translations is that the meanings of words change over time, as can be clearly seen by examining the way the Hebrew word sheol is treated.
Here's a chart of how sheol is translated in different versions of the Bible. This chart doesn't explain any of the other differences between the translations or why one should one over another, other than to mention that the person who compiled the chart is a Jehovah's Witness who believes that the New World Translation (NWT) is the most faithful to the original.
With a WFW translation it's very easy to think you understand the thought behind a word but be entirely mistaken. Some readers prefer WFW translations because they don't want to trust translators to attribute the right thoughts to the words... but they're still trusting the translators to put the right English words to the original words. It seems to me that even if you learn the original languages yourself you're still going to have to trust that your teachers are teaching you the language properly. Since you can't escape trusting someone, I prefer to cut out all the middle steps and just buy a TFT translation.
You might want to read "Truth in Translation: Accuracy and Bias in English Translations of the New Testament" by Jason BeDuhn ISBN: 0761825568.
It compares nine important recent Bible Translations: The Amplified NT; The Living Bible; New American Bible with Revised NT; The New American Standard Bible; New International Version; New Revised Standard Version; New World Translation; and Today's English Version (Good News Bible).
By looking at passages where theological investment is at a premium, the author demonstrates that many versions deviate from accurate translation under the pressure of theological bias.
I use the NIV for everyday reading. It's my main bible, but if I'm doing serious indepth study I always start by reading the passage in multiple versions.
Back when I was in Bible grad school I asked the leading translation scholar at our school which version was best. He said if you want WFW the RSV was the best but if you wanted Paragraph for Paragraph, the NIV was better at catching the full thought.
He carried a greek bible. :)
A friend of mine used to work for the Lockman Foundation, which did the NIV translation. He said that the translators (who came from a variety of faiths) would spend an incredible amount of time making sure that they did an accurate translation, not only at the idea level, but at the word level. In some cases, they argued for months about how to translate one word--and still didn't reach consensus on it.
Bias is inevitable in translating an ancient text where we have only a limited number of other texts in the same language. My Ancient Near East professor made the point that the assumptions that you bring to the problem influence the results. If you assume that the whole Old Testament was written down at about the same time, then you make assumptions about a common meaning to certain words. If you assume that different books were written at different times, then the same word might have genuinely different meanings in different places.
To get an idea of the complexity of this problem, go find all uses of the verb "ratsakh" in the Old Testament. In some contexts, it seems to mean "to kill" such as killing animals. In other contexts, when it refers to people, it really only makes sense to translate it as "to murder"--others the prohibition on murder in the Ten Commandments contradicts the Levitical code provisions for the death penalty.
I've often wanted to study Bible translation, but it's a daunting task. The best easy solution I've found is a parallel Bible, which lines up four different translations side by side.
There are online Bibles that will line-up passages for comparison. Try:
http://unbound.biola.edu/