Ooh, good one. And similarly, Fanfare For The Common Man by Aaron Copland.
ETA: in fact a lot of Copland is very “American”, but particularly patriotic oriented would be his “Lincoln Portrait”. Get the reading by James Earl Jones, it’s teh awesome.
New World Symphony by Dvorak.
Violent Femmes-American Music.
There are of course, the originals…The Star Spangled Banner, America, America the Beautiful, God Bless America, Hail Columbia, and Columbia, Gem of the Ocean. Also, how about someSousamarches?
I’ll probably throw in a couple of tracks along those lines. Mainly, though, I’m going for rock, country, soul… American genres singing about America, that sort o’ thing… And a novelty or two, like:
Heh. I’ve already downlaoded “I’m just a Bill.” Somehow I didn’t think of this one. Maybe I’ll do both. 
Some great ideas so far; thanks to all and keep 'em coming!
Not to mention “You’re a Grand Old Flag” and “This Is My Country”.
Then there’s Robert Russell Bennett, who wrote all manner of American-themed orchestral music, such as “Victory at Sea”, “Armed Forces Suite”, “Suite of Old American Dances”, “Abraham Lincoln: A Likeness in Symphony Form”, and “Symphony in D for the Dodgers” (incorporating speeches by sportscaster Red Barber).
Ry Cooder also does a heartwarming take on The Battle Cry Of Freedom. His cover of Comin’ In On A Wing And A Prayer gets me dewy eyed every time.
You really won’t have a complete set without some version of Little Steven’s I Am A Patriot. Somehow, I haven’t heard Little Steven’s own version, but David Lindley does it. Jackson Browne sang it on stage, opening for Bonnie Raitt, but I don’t know if he ever recorded it.
Eh, I shoulda known, YouTube has nearly everything. Three versions of Little Steven singing I Am A Patriot, more by Jackson Browne, and two by Eddie Vedder. Vedder sings the line as “I was talking with my boyfriend,” (is Vedder gay? I did not know that.)
There’s 27 Ry Cooder vids, some of them breathtaking, but not Battle Cry or Wing And A Prayer.
“Promised Land”, by Chuck Berry.
“Some Gave All”, by Billy Ray Cyrus. (Don’t laugh. It’s much better than “Achy Breaky Heart”.)
America - Niel Diamond
American Girl - Tom Petty & The Heartbreakers
American Girls - Counting Crows
American Idiot - Green Day
American Woman - Lenny Kravitz
American Woman - The Guess Who
Born in the USA - Bruce Springsteen
The Hands that Built America - U2
Heartland - U2
Little Pink Houses - John Mellancamp
Living in America - James Brown
I haven’t even included angry American songs
So’s a busted leg, so what?
“John Walker’s Blues” by Steve Earle
“The Traveling Soldier” by the Dixie Chicks
“Ain’t Nobody Better Than Us” by Leadbelly
“Rhapsody in Blue” by George Gershwin
A previous thread that may be of interest: Need ideas for Election Night party mix CD - NO LEE GREENWOOD! - Cafe Society - Straight Dope Message Board
U.S Marine Corps Hymn
That one’s a little angry. 
I would characterize “American Idiot” and the Guess Who’s “American Woman” as pretty blatantly critical of the USA… not selections I would expect to find in a “patriotic” mix. (Along the same lines, I was thinking of suggesting the Steve Miller Band’s “Living in the U.S.A.” but didn’t – great song, but not really patriotic.)
Here’s another odd one: Steppenwolf’s “Monster”. Sort of “I love my country and that’s why I’m protesting what it’s turned into”.
Probably crosses over in the treacly category (although definitely not crap):
Tim McGraw - If You’re Reading This
Heartfelt and touching IMHO.
“Forty Hour Week (For a Livin’)” - Alabama
Good choice on leaving out “God Bless the USA”, since if you actually listen to the lyrics, it’s about how unimportant freedom and democracy and the like are to the narrator. Unfortunately, I don’t think anyone, including the writer, pays enough attention to the lyrics to realize that.