1. "Jesus is all the world to me, My life, my joy, my all; He is my strength from day to day-- Without Him I would fall.  When I am sad to Him I go; No other one can cheer me so; When I am sad, He makes me glad: He's my Friend.
  2. "Jesus is all the world to me, My friend in trials sore; I go to Him for blessings and He gives them o'er and o'er.  He sends the sunshine and the rain; He sends the harvest's golden grain; Sunshine and rain, harvest of grain: He's my Friend.
  3. "Jesus is all the world to me, And true to Him I'll be; O how could I this friend deny, When He's so good to me?  Following Him I know I'm right, He watches o'er me day and night; Following Him, by day and night: He's my Friend.
  4. "Jesus is all the world to me, I want no better friend; I trust Him now, I'll trust Him when Life's fleeting days shall end.  Beautiful life with such a Friend, Beautiful life that has no end; Eternal life, eternal joy: He's my Friend."
(Words by Will L. Thompson)
Beginning with our Prime Directive "checkoff list", we can see that this is a psalm of praise extolling God's power and work and a hymn that teaches our dependence on Him and His willingness to bless.  
Will L. Thompson (1847-1909) earned a degree in business from Alliance College in Alliance, Ohio (no doubt influenced by his father who was a successful merchant), but had shown an interest in music from an early age, having written several songs before graduating high school.  He furthered his musical education, graduating from the New England Conservatory of Music as well as studying music in Leipzig, Germany.
As a young man, Thompson sent a package of four songs to a publisher, requesting payment of $100 for the entire package.  When the publisher responded with a counter-offer of $25, Thompson declined.  Since he couldn't get what he considered to be a fair price for his music, he decided to go into business for himself and started a music store in East Liverpool in association with his father's business.  He also went into the mail order business, selling sheet music and music books.  He became successful with this, so much so that he became known as the millionaire "Bard of Ohio."
While attending an evangelistic meeting, he decided to devote himself to writing, selling, and promoting Christian music.  In 1880, he wrote "Softly and Tenderly", which became popular rather quickly as a hymn of invitation.  "Jesus is All the World to Me" achieved similar popularity soon after it's writing in 1904.
This song does seem to make some rather lofty claims, so we should see how well they match with Scripture.
Every verse begins with "Jesus is all the world to me," and the first verse continues with "my life, my joy, my all."  I believe we can assign this as artistic license, demonstrating how important the Lord is (or at least should be) in one's life.  The verse continues, "He is my strength from day to day, Without Him I would fall."  First of all, it is safe to say that Jesus is God (John 17:11; Philippians 2:5-6) and as we learned from the song "Let Him Have His Way with Thee", we learn from Jude 24 and 2 Peter 1:5-10 (emphasis on verse 10) that He is able to keep us from falling.  The verse goes on to say, "When I am sad, to Him I go; no other One can cheer me so; When I am sad, He makes me glad!"  As we also discussed in "Follow Me," Jesus does still speak to us through the Bible (John 16:12-13; 2 Timothy 3:16-17; 2 Peter 3:15-16), so we can "go to Him" through His Word to receive encouragement (cheer).
The second verse describes the Lord as, "My friend in trials sore," and goes on to say, "I go to Him for blessings and He gives them o'er and o'er.  He sends the sunshine and the rain; He sends the harvest's golden grain; Sunshine and rain, harvest of grain."  As was mentioned earlier, since Jesus is God, He also sends sunshine and rain (Matthew 5:45-46) [I'm not certain if "[going] to Him for blessings" is akin to prayer; as I understand it, we pray to God the Father by the authority of and through Jesus (John 14:6; 15:16); this is part of the problem I have with songs like "Have a Little Talk with Jesus" and "Tell It to Jesus Alone"; if I am mistaken on any of these points, I do ask for clarification, please].
In the third verse, the promise is made that "true to Him I'll be."  However, when the line is sung, "Oh, how could I this friend deny, When He's so good to me?" I hope it is rhetorical; after all, we do have the example of Peter (Matthew 26:69-75; Mark 14:66-72; Luke 22:54-62; John 18:15-18, 25-27).  But the verse goes further: "Following Him, I know I'm right; He watches o'er me day and night; following Him by day and night."  Again, Jesus is God, so He does not sleep (Psalm 121:4) and He is constantly praying to the Father for us, interceding on our behalf (John 17:9, 20-21). 
The final verse makes an exceptionally good promise: "I want no better friend.  I trust Him now, I'll trust Him when Life's fleeting days shall end."  It also looks forward to a "Beautiful life with such a friend, Beautiful life that has no end; Eternal life, eternal joy."  The promise can be verified by what Jesus told John in Revelation 2:7, 10, 17 and Revelation 21:1-7: eternal joy awaits us if we have been faithful.
This brings me to the final statement which closes every verse of this song, and considering we are singing about Someone who helped create all that there is, it is quite a lofty claim: "He's my friend."  This could seem presumptuous, possibly bordering on arrogance, as anyone can claim to be a friend of somebody else.  But can that claim be reciprocal, particularly in this case?  Can Jesus call us friend?
Fortunately, the Messiah Jesus Himself gives this answer in John 15:14: "You are my friends if you do what I command you."  And as we saw in our analysis of the last stanza, if we do as He commands us and we are faithful to the point of death, we will get to see "eternal life, eternal joy" with Him, our Friend.
As always, I welcome your thoughts…

--updated 8/31/2015