What are some key themes in Walt Whitman's poetry?

I think that Whitman was something of a mystic in that he saw all of us as part of the whole; but it was the democratic whole.  He saw himself as the poet that Emerson called for; Emerson saw him as the poet who answered his challenge.

This yields two themes:  the unity of all being (and, if you read his endless lists of "things," none of which are subjugated to another but all treated as equal you understand where this is coming from.  The other is American as the fulfillment of the democratic idea.  This is similar to his mystical view of the unity of all things, but is more political, more based in the reality of what he saw and lived with.

Indians, blacks, Irish, gays, straighs, men, prostitutes, laborers, women, old, young ... these were all part of the theoretical unity of being, expressed in the structure of America.

Walt Whitman wrote of the divinity of the self (the "I" in his poems has been reborn as something divine) and of the individual as well as the community of man as in his "Leaves of Grass."  Whitman was his speaker in "Leaves of Grass":

I am the poet of the Body and I am the poet of the Soul...
I am the poet of the woman the same as the man...
I am not the poet of goodness only, I do not decline to be the poet fo wickedness also ("Leave of Grass").

He also had themes of exploration and exaltation of sexuality, themes which brought much criticism upon him. Nature and its beauty are among themes treated by his poetry as are the melancholy and horrors of death in the Civil War.  He received high acclaim for his elegy written after the slaying of Abraham Lincoln:  "O Captain! My Captain!"

What are the major themes in Whitman's "Song of Myself"?

This long poem, a piece of Leaves of Grass, is a spontaneous self-portrait in prose form, celebrating Whitman’s individuality while acknowledging how all humanity is alike (like “leaves of grass”). 

“I harbor for good or bad, I permit to speak at every hazard,/
Nature without check with original energy.”

Whitman’s consistent and unequivocal comment on life is to live it, every day, every moment, to savor and enjoy and be ultra-conscious of your own facticity:

 “My respiration and inspiration, the beating of my heart, the
     passing of blood and air through my lungs,
The sniff of green leaves and dry leaves, and of the shore and
     dark-color'd sea-rocks, and of hay in the barn,”

A second, related theme is that the universe is infinite, that our immediate existence is but a fraction of all that is:

     “You shall possess the good of the earth and sun, (there are
     millions of suns left,)”

Whitman’s “song” is that there is no limit to our experience as living creatures, as spirits given the blessing of our existence.  While it is difficult for us as common men to see the grandeur, Whitman manages to point to it and invite our souls to celebrate the fact of being.

These themes are so large in concept, so vital to our understanding of Whitman's life-message, that paraphrasing or condensing them is "murdering to dissect,"  that is the "life" of the poem itself is diminished; reading the poem is all the "analysis" you need in order to understand his connection to the reader.