John, son of Zebedee
A good deal of modern theological analysis supports the presumption that John of Zebedee wrote this gospel. This is almost invariably speculative and tends to use circular reasoning: for example, proponents believe that the Gospel was written around 80-90 CE and also believe that John lived into his nineties at least, so he could have written the gospel that now bears his name. Or that we think the book was written in Ephesus and the apostle John is the only John of Ephesus of whom anything is known - thus jumping from a presumption that the book was written in Ephesus to a presumption that the author was called John and finally that he must have been the apostle John because a late tradition links John to Ephesus. None of this is external evidence in an objective sense.
Urban C. von Wahlde (The Gospel and Letters of John, Volume 3, page 412) says that Irenaeus was the first to mention the apostle John as the author of the Gospel, saying that his information came from Polycarp. von Wahlde sees more significance in the absence of early references to John as author than he sees in Irenaeus' report, since the accuracy of his report is in doubt on other grounds. In short, von Wahlde says there is no reliable evidence that John, son of Zebedee was the author of the Gospel.
John of Patmos
Now, we should also rule out the author of Revelation as the author of the John's Gospel. The author of Revelation actually identifies himself as a person called John, but the author of the fourth gospel chose to be anonymous. It would be flawed reasoning to say that because the Gospel was eventually attributed to the apostle John that any other important early Christian author named John must also be the apostle John. The theology and style of Revelation are far removed from the theology and style of John. Burton L. Mack says in Who Wrote the New Testament, page 197, that even after the Book of Revelation was blessed for posterity by inclusion in Athanasius' list of apostolic writings, there were doctors of the church who questioned its authenticity and groused about its theology. Wikipedia tells us that Dionysius of Alexandria noted that the gospel and the epistles attributed to John, unlike Revelation, do not name their author, and that the Greek of the gospel is correct and elegant while that of Revelation is neither. So, today, scholars tend to refer to the author of Revelation as 'John of Patmos' to distinguish him from either the apostle John or the author of John's Gospel.
John the 'elder'
It can be argued that the author of the Johannine epistles wrote, or at least contributed to John. Wikipedia points out the phraseology of the first letter of John is very similar to that of the fourth gospel and the two works use many of the same characteristic words and phrases, such as light, darkness, life, truth, a new commandment, to be of the truth, to do the truth and only begotten son. In both works, the same basic concepts are explored: the Word, the incarnation, the passing from death to life, the truth and lies. The two works also bear many stylistic affinities to one another. In the words of Amos Wilder, the works share "a combination of simplicity and elevation which differs from the flexible discourse of Paul and from the more concrete vocabulary and formal features of the Synoptic Gospels. The three Johannine epistles appear to be from the same author, who remains nameless but calls himself 'the elder' (or presbyter) - see 2 John 1; 3 John 1. This 'elder' certainly was not the apostle John or any other apostle, since it is inconceivable that an apostle would simply designate himself as the elder when writing to people who knew him to be far more than a presbyter.
In conclusion, we are on reasonably safe ground in saying that the author of the three Epistles of John wrote or, more likely, contributed to the authorship of John's Gospel. This author remains anonymous in the epistles, but styles himself as the elder, or the presbyter.