Even without the the "aww" factor that he wrote the song for one of his sons (or the "uh" factor when you realize that Lennon didn't spend a great deal of time with his first son, Julian), the lyrics are still powerful and moving. There is a sweetness and optimism in the song that wasn't always present in Lennon's work (see "Happy Xmas (War is Over)" for a true example of a real downer from the Lennon songbook). Besides my favorite part ("Before you cross the street/ Please take my hand/ Life is what happens to you while you're busy making other plans"), the assertion that "Every day in every way/ It's getting better and better," which many take as a homage to Paul McCartney's lyrics in the Beatles' song "Getting Better," illustrates Lennon's sense of hope.*
While the song has been covered by many singers (Freshly Ground, Ben Harper, and *shudder* Celine Dion), Lennon's version is the gold standard. However, if you want to see something completely manipulative and sentimental yet still oddly touching, check out Richard Dreyfuss's take on the song from Mr. Holland's Opus. Vocally, Mr, Holland would be cut down by Simon Cowell, but there is something that works about the performance.
*For the record, McCartney's chorus for "Getting Better" is "I have to admit it's getting better/ A little better all the time." Lennon, who was always the more cynical of the two, added "It can't get no worse."