We don't consider ANY translations, no matter who they are done by to be accurate. Ones done by non-Jews are particularly suspect since they fail to take into account the fact that a single word in the text could have widely divergent meanings dependent on context and the type of interpretation being used.
See, there are four main ways to study any part of the Tanakh (what you would refer to as the Old Testament but without Revelations and chapter/verse and sometimes even book splits vary).
1) pshat- the straight literal meaning
2) remesh- the alluded to meanings in the passages
3) Derash- often linked to the meaning in the midrash - some legalistic and some allegorical
4) sod- literally meaniong secret, often called Kaballah and refers to the hidden mystical meaning behind the actal text.
So, now a translator needs to know WHICH version to use in order to bring out the correct meaning! Obviously, a translator not knowledgeable in the various facets, is not going to get it right, so Jews don't see it as possible for a non-Jew to do a translation of the Tanakh.
About the best translation there is to get the meaning is the one by Artscroll/Metsorah publications- they generally stick to the pshat understanding as given by Rashi (a major commentator from the 12th century). In their translation of the Torah (the Five Books of Moses), they have also done one which is more in line in line with Ramban and thus the translation tends to be more in line with remesh/derash understandings. In many cases it does not vary- in some cases the variance does not look like much, but the nuance implies a lot!
Overall- we study and read the Tanakh in Hebrew- we don't rely on translations due to the fact that they miss the essence in trying to render the complex into the simplistic.
edit: The Old testament is roughly analogous to the Tanakh. The differences are
1) different verse and chapter breaks
2) Different book breaks
3) The book of Revelations is NOT in the Tanakh
4) The Apocryphy and Pseudographia are not in the Tanakh
Good translations are the Artscroll Metsorah translation. The Tanakh is excllent, there are also editions with translated Rashi, Baal HaTurim and Ramban (only partially released) of the Torah. Each of these have slightly different translations as each of these commentaries is concentrated on a diffrent method of interpretation (Rashi on Pshat, Ramban on remesh/derash and the Baal HaTurim, as a student of ramban, on areas that ramban didn't comment on such as Gematria and many of the notes of the Masortes.) An excellent translation of both the Torah and the Ramban commentaries has been done by Rabbi Chavel, though I don't know who the publisher is,