"With Show Boat a new art form emerged in the American musical theatre for the first time: the musical play as distinguished from musical comedy," reads one description of Show Boat. "Here was a rich, colorful, nostalgic chapter from the American past filled with humour, gentle pathos, tenderness and high drama. It bewitched the eye, ear and heart. It was a revelation; and it was a revolution." (Source)
Before Show Boat, American musicals had typically been comedies, accenting a generally light mood with musical and dance numbers and using flowery, poetic language. By creating a show with serious content and believable, three-dimensional characters, Jerome Kern and Oscar Hammerstein II helped kick off a new phase in musical theater writing.
Writing for musical theater is a tricky art. The songs have to be light enough to be entertaining but serious enough to closely follow a plot. For Hammerstein to create lyrics that not only told a story but also placed the whole story in a historical setting with complex racial dynamics was no small task. "Ol' Man River" epitomizes this achievement.
"Hammerstein's is an unobtrusive craft, an artless art," wrote Mark Steyn for Slate. "'Ol' Man River' was the song in which he first found his lyrical voice, compressing the suffering, resignation, and anger of an entire race into 24 taut lines and doing it so naturally that it's no wonder folks assume the song's a Negro spiritual." (Source)
There are subtler factors than the lyrical topic that make "Ol' Man River" powerful. As Steyn points out, the song does not hit a proper rhyme until the 8th and 10th lines ("cotton" and "forgotten"), leaving the rest to musical flow and avoiding the cheesy, overstated feeling that too much rhyme can sometimes give a song. The song also makes use of a consistent and obvious central image, the river, to make subtler statements about the condition of the singer and his surroundings. The singer compares his condition to that of the river and determines that the river is more free and at peace than he will ever be.
The lyrics have undergone several changes to keep up with the times and make the song accessible to new audiences, but the essence has remained. "Ol' Man River" is also generally written out without the stereotypical "Black speech" style it was written in back then (and you'll notice that, for the most part, Paul Robeson didn't actually sing it that way anyhow). With those changes only strengthening it, the power of the songwriting remains for many people today.