The next day he saw Jesus coming toward him, and said, “Behold, the Lamb of God, who takes away the sin of the world! (John 1:29 ESV)
(For a better and more recent defense see here.)
Those who advocate the doctrine of Unlimited Atonement obviously take “world” everyone who has lived or will live, all without exception. Not world in the sense of many people, not world in the sense of from every “tribe and language and people and nation” as Revelation 5:9 would put it
Here is what the ESV MacArthur Study Bible says: 
John 1:29 The next day. This phrase probably refers to the day after John’s response to the Jerusalem delegation. It also initiates a sequence of days (v. 43; 2:1) that culminated in the miracle at Cana (2:1–11). the Lamb of God. The use of a lamb for sacrifice was very familiar to Jews. A lamb was used as a sacrifice during Passover (Ex. 12:1–36); a lamb was led to the slaughter in the prophecies of Isaiah (Isa. 53:7); a lamb was offered in the daily sacrifices of Israel (Lev. 14:12–21; cf. Heb. 10:5–7). John the Baptist used this expression as a reference to the ultimate sacrifice of Jesus on the cross to atone for the sins of the world, a theme which John the apostle carries throughout his writings (John 19:36; cf. Rev. 5:1–6; 7:17; 17:14) and that appears in other NT writings (e.g., 1 Pet. 1:19). sin of the world! See note on John 1:9; cf. 3:16; 6:33, 51. In this context “world” has the connotation of humanity in general, not specificall...