Why were verses taken out of the Bible when it was being formed? Was there any major stuff taken out? I've heard that during the Roman times (AD) when the Bible was first being put together that a lot of texts and scriptures weren't allowed to go into the Bible. I just wondered why this would be and if there were any major scriptures taken out? (By major I mean stuff that would actually redefine the Bible itself).
Yes, some books of the Bible had a harder time than others getting into the New Testament we have today (all 27 "books"). I believe, however, the Holy Bible we possess today, however, comprises all that God wanted it to comprise. Nothing has been "left out," as you put it. 

God's word was certainly inspired by the Holy Spirit (2 Tim 3:16), but it was also  preserved from the very beginning, I suggest, by the same Holy Spirit. Ever since it was penned it has been dynamic, living, and powerful (Heb 4:12), containing as it does all that is needed for a life which is pleasing to God (2 Pet 1:3). Ever since it was penned it has encapsulated and preserved the 


  ". . . faith which was once for all handed down to the saints (Jude 1:3), 


both in written and--let us not forget--spoken forms, since one of the most important spiritual gifts beginning on the Day of Pentecost was the gift of prophecy, which is the foretelling and forth-telling of God's word! 

How the Bible came to us is a subject well worth investigating, and I suggest you go here for a nice overview of that fascinating process. That link will take you to other helpful sources of information, including F.F. Bruce's fine book and other valuable tools.

The canon of Scripture came about slowly but surely, with many twists and turns, as believers convened many different colloquies over many years to discuss "what stays in and what stays out." I believe God's Holy Spirit, just as He inspired the writers of Scripture to write what they wrote, also superintended the process of canonization, so that the Bible we have today is exactly what God wanted us to have. The Bible's internal consistency bears witness, I believe, to the supernatural origin and preservation of Scripture. 

Having said this, and more apropos your answer, there were two major kinds of colloquies. The first kind focused on which books "should make it" and which books "shouldn't make it." Second Peter had a particularly hard time making it into our Bible, because as Nelson Publishers NASV Updated Edition noted in their NASB Visual Reference Bible,  


  "No other book in the New Testament poses as many problems of authenticity as does 2 Peter" (p.1355). 


The Muratorian Canon, based on an ancient list of 24 of the 27 books of the NT and compiled in Latin by L.A. Muratori, provides us with significant evidence that the early Councils of the Christian church, such as the Council of Laodicea (AD 363), were "on the right track" in recognizing the authoritative nature of the 27 books of what we today call the New Testament. Other Councils followed, such as the Council of Hippo (A.D. 393) and the Council of Carthage (A.D. 397), both of which also affirmed the same 27 books as authoritative. Again, read more, here.

The second kind focused on how to translate into whatever language the committee chose (whether English, Swahili, Tagolog, Chinese, Aleut, ad infinitum), the books which had already "made it" into the canon of Scripture. These gatherings, or committees, of Bible scholars translated the canon of Scripture by using whatever texts were at their disposal, some ancient and some not so ancient. 

A famous text for the New Testament, for example, is the Nestle-Aland text which is now in its 28th edition! The scholars involved in this project took it upon themselves to do critical editing of the original Greek-language version of the NT, the Novum Testamentum Graece. The resulting Nestle-Aland text is the primary source today for modern NT translations, thanks to people such as Cardinal Cisneros and also Erasmus, who produced the first published edition of the Greek New Testament in 1516. 

The many translation committees which have convened down through the years were guided, I believe, by the Holy Spirit of God in providing average, ordinary people (some of whom were not even literate and had to rely on hearing the Word of God read to them) with the inestimable privilege of reading and hearing God's special revelation, despite the irrational opposition of the powers that be among authoritative leaders of "the church's" hierarchy. The story of organized opposition to the translation of God's word into the "language of the people" is alternately fascinating, inspiring, and appalling, given the sacrifices many brave men and women made, to the point of losing their very lives on account of their commitment to make Scripture available to people everywhere.

I wish you well in your investigation into the fascinating subject of the process through which our Bible came to us. Both "testaments" came about in slightly different ways, but the end result was (and continues to be) a reliable, trustworthy document, which is not only a perennial bestseller in scores of languages, but has the power to transform the lives of all who read it. 

Is the Bible "perfect" in every way? No. Translators have always disagreed and will continue to disagree on the minutiae of how best to translate a given word, or verse, or even an entire passage from the original languages of Hebrew, Aramaic, and Greek. 

The upside of all this, however, is that Christians today have an embarrassment of riches of Bible versions, not one of which disagrees with another on any significant and indispensable doctrine of the Judeo-Christian faith which was once and for all delivered to the saints (Jude 1:3). 

There may be a version or two, here or there, which deliberately tamper with God's word, such as Thomas Jefferson's expurgated version of the New Testament, which excised all the miracles recorded in the four Gospels, as well as every reference which asserted that Jesus was divine (see here). By and large, however, we have never had such a wealth of Bible-study tools at our disposal (and at the speed of light!), than we do today, thanks to the internet. Praise the Lord!