What evidence is there that John was aware of the Synoptics when he wrote the Fourth Gospel?
One thing we might note is the familiarity with parts of the Synoptic tradition which the author assumes of his reader. For instance, in John 1:40, the author introduces Andrew as Simon Peter's brother before having introduced Simon Peter. In 2:1f the author speaks of Jesus' mother, never introducing her as Mary. And in John 11:1-2 Lazarus is introduced as being from Bethany, the village of Mary and her sister Martha. The author elaborates that it was the Mary who annointed the Lord with ointment and wiped his feet with her hair - a story which isn't recounted in the same Gospel for another chapter.
Andreas Kostenberger in his Theology of John's Gospel and Leters makes what is in my opinion a strong argument that John positions himself (also cf. John 1:18 and 13:23) to give a supplemental view to the Synoptics which plays out in the transposition of many of the major Synoptic themes:
He lists about twenty or so of these transpositions, some more convincing, some less. But the overall effect is to build a persuasive case that the author of the gospel intentionally wrote the gospel to supplement what was already in the Synoptic tradition. Essentially the Fourth Gospel's silence on so many of the key events and themes in the Synoptics diminishes the chances that it could be accidentally different.
The fourth evangelist must have known the basic literary structure of Mark's Gospel: Starting with John the Baptist, baptism of Christ, the call of the disciples (Joh 1:35-51) and ending with Passion and Resurrection of Christ.1
Some more compositional analogies:
There are also some analogies with Luke:
Though there are some who try to give reasons for a chronological priority of John before the synoptics2, a majority assumes that John had known the synoptics.
1: Petr Pokorný, Ulrich Heckel, ''Einleitung in das Neue Testament'' , 547ff.