Actually, the KJV is a paraphrased version as well. As a matter of fact, in many areas the NIV is more literal than the KJV, and in ways that are not all trivial. Sure--while shoe latchets and wine bottles, which didn't exist in Jesus' life, are details that are not so important (but they are conclusive proof that the NIV is more literal than the KJV in those areas), though the term "wineskins" helps us understand the culture better.
The NIV DOES, however, use the terms "Hades" and "grave" in those areas where the grave is mentioned in the scriptures, where the KJV just blankets everything with a universal word "hell" and is done with it, for the most part. This is an extremely important difference between the two, as likening Sheoul and Hades to be the same concept as Gehenna has cost us dearly in our understanding of things.
Still, neither the NIV nor the KJV is perfect, as no human translation is. If you're looking for a more literal translation, I'd say the NAS is closer to such a thing than either, although, as stated before, it still contains some of that old traditional atmosphere to its style.
For a "full meal deal," though, if you're looking for a LITERAL translation, I say get a copy of the Scriptures, from the Institute of Scripture Research. It is the most literal translation I have seen--it lets EVERYTHING hang out, with no pleasantries, and no traditional styles to get in the way. If there is any debate, the original word is left intact and an analysis is written in the appendix. This applies to Elohim, El, El Shaddah, Yeshua, Yahweh, and all other names of God. No translation is completely literal--sentence structures, verb-nouns, and conjugations prevent such a dream. But this is as close to literal as it gets.