Why do some Bible Translations omit John 7:53-8:11? When I tried to look at the verses quoted in this question Ihttp://christianity.stackexchange.com/questions/5903/what-did-jesus-write-on-the-ground/
I found that in the New World  Translation of the Holy Scriptures  John 7 ends at verse 52 and John 8 starts with verse 12 so the whole story about Jesus writing in the dust and saying let he who is without sin cast the first stone does not exist in this translation 
A foot note states that many consider the omitted verses to be of questionable sourcing 

Why would some bibles have these verses and others leave them out?
The simple answer is that there are some older manuscripts that lack the reading.  If credence is placed in the older manuscript, then the reading is left out.  The assumption is that the older manuscripts are closer to the source documents.

By the way, many view the New World Translation with suspicion. It is a product of the Watch Tower Bible and Tract Society (Jehovah's Witnesses.) From what I've heard, there isn't much known about how they created the translation.