The ἐγώ εἰμι sayings in the gospel of John are famous. The phrase occurs 21 times. Jesus says that "I am" the Bread of Life (6:20, 35, 41, 48, 51), the Light of the World (8:12), the Gate (10:7, 9), the Good Shepherd (10:11, 14), the Resurrection and the Life (11:25), the Way (14:6), and the True Vine (15:1, 5).
These are significant in that they are a reflection of the divine name in Exodus 3:14, where the God of the burning bush answers Moses' question about his name. In the LXX we read, Ἐγώ εἰμι ὁ ὤν, "I am who I am" (ESV).