I believe that the Bible teaches the Trinity.
Regarding the Scripture references, probably, the most clear one is 1 John 5:7: “For there are three that bear witness in heaven: the Father, the Word, and the Holy Spirit; and these three are one.” However, there is a serious textual problem with the second part of this verse (“the Father, the Word, and the Holy Spirit; and these three are one”). Only several late manuscripts include this part. All the other Greek manuscripts, including all the early ones, do not contain it. Because of this reason, most scholars do not consider it to be a part of the original Greek text. It is not included into the modern editions of Greek New Testament (Nestle-Aland Greek New Testament (GNT), UBS (United Bible Societies) GNT, and even The Greek New Testament According to the Majority Text which mainly follows Textus Receptus (TR) that contains this phrase). Most modern translations of the New Testament do not have it either.
Another Scriptural reference is Matthew 28:19: “Go therefore and make disciples of all the nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit.” Here, “the name” is singular and is “of the Father and of the Son and of the Holy Spirit.” It is important that the word “the name” is singular, not plural, that is, it is not “the name of the Father, the name of the Son, and the name of the Holy Spirit.” Here, there is only one name of the one God, and this name is “the Father, the Son, and the Holy Spirit.” This indicates that the Father, the Son, and the Holy Spirit are one.
However, if we take only Matthew 28:19, it may lead us to modalism (the belief that the Father, the Son, and the Holy Spirit are three stages or moduses of God and they do not exist simultaneously). Matthew 3:16-17 denies this view: “16 When He had been baptized, Jesus came up immediately from the water; and behold, the heavens were opened to Him, and He saw the Spirit of God descending like a dove and alighting upon Him. 17 And suddenly a voice came from heaven, saying, “This is My beloved Son, in whom I am well pleased.”” Jesus, the Son, was standing on the earth, the Spirit of God descended upon Him, and the Father was speaking from the heavens.
Another way to see that the Bible teaches about the Trinity is to consider several verses together and use some logic. 1) The Bible says that there is only one God (Deut. 6:4; 1 Cor. 8:4-6). 2) The Bible also says that: a) the Father is God (John 6:27; 1 Pet. 1:2), b) the Son is God (John 1:1; Rom. 9:5), c) the Holy Spirit is God (Acts 5:3-4). So, on the one hand, there is only one God. On the other hand, the Father is God, the Son is God, and the Holy Spirit is God. The logical conclusion is the doctrine of the Trinity.
Of course, the New Testament speaks about the Trinity much more clear than the Old Testament, though the Old Testament has some hints. Many scholars consider the plural number of the Hebrew word for God (Elohim) and the words “Us” and “Our” in Genesis 1:26; 3:22; 11:7; Isaiah 6:8 as an indication of the Trinity. However, many consider that these are cases of majestic plural (http://en.wikipedia.org/wiki/Majestic_plural). In the Quran, Allah often speaks “We” when referring to Himself. Such cases are much more numerous than in the Old Testament, but no Muslim has ever thought that they indicate the Trinity. All the Muslims agree that such cases are majestic plural. Hebrew and Arabic are both Semitic and have many things in common. However, majestic plural was used not only in Semitic languages. Kings of some countries used the form “we” instead of “I”, speaking about themselves. In many languages, there is a custom to use the pronoun in the plural form of the 2nd person or of the 3rd person, addressing to one person. In English, it became so usual that the original singular form of the 2nd person was practically lost: originally, “you” was the plural form and “thou” was the singular form, but now “thou” is practically not used. This custom also has to do with majestic plural. So, majestic plural is quite common in many languages and cultures, and it is not a wonder if it was in the Old Testament.
However, there are some verses in the Old Testament that seem to indicate that there are more than One Person in the Godhead. For example, Psalm 45:6-7: “6 Your throne, O God, is forever and ever; A scepter of righteousness is the scepter of Your kingdom. 7 You love righteousness and hate wickedness; Therefore God, Your God, has anointed You With the oil of gladness more than Your companions.” Psalm 110:1: “The Lord said to my Lord, “Sit at My right hand, Till I make Your enemies Your footstool.”” Zechariah 3:2: “And the Lord said to Satan, “The Lord rebuke you, Satan! The Lord who has chosen Jerusalem rebuke you! Is this not a brand plucked from the fire?”” Isaiah 48:16: “”Come near to Me, hear this: I have not spoken in secret from the beginning; From the time that it was, I was there. And now the Lord God and His Spirit Have sent Me.””
Anyway, the Old Testament has only some hints regarding the Trinity. The New Testament is quite clear regarding the Trinity.