The rules…
Cannot be state anthem
State must be mentioned by name in title of song
Hi, Opal!
For my home state, Mississippi, I can only think of two: Mississippi Queen and Louisiana Woman, Mississippi Man. I’m sure there are others but they’re not coming to me.
International Dopers are allowed to use songs featuring their home parishes, oblasts, areas, regions, stadts, or autonomous territories.
Georgia on My Mind
Midnight Train to GA
That’s the Night That the Lights Went Out in GA
The Devil Went Down to GA
Sweet GA Brown (Ok, not exactly about the state)
~J
And for TX, where I currently reside:
All My Exes Live in TX
God Bless Texas
Yellow Rose of Texas
God Blessed Texas
The Bluest Eyes in Texas
Texas Women
There are at least DOZENS more about each state, but those are the ones I thought of rather quickly that mention the state in the title.
~J
Current state of residence:Virginia Plain by Roxy Music
Birth State: Johnsburg, Illinois by Tom Waits
Can’t really think of too many songs that have Illinois in the title.
British Columbia: The Lumberjack Song.
Pennsylvania 6-5000
Hotel California
California, Here I Come
Going Back To Cali
My home state, South Carolina, gets shortchanged, as does our neighbor to the north. Most of the song titles have simply “Carolina” in the title:
“Carolina in My Mind”
“Carolina Dreams”
At lease our state song has it right - “South Carolina on My Mind.”
Sweet Home Alabama. There are many others, but I’ll leave it at that. 
Nichol_Storm: Here’s a little help fer ya’, Neighbor: Miss The Mississippi by Emmylou Harris.
But my favorite song about Mississippi is this one:
Mississippi in the middle of a dry spell
Jimmy Rogers on the radio up high
Mama’s dancin’ with baby on her shoulder
Sun is settin’ like molasses in the sky
From Black Velvet as performed by Alannah Myles and others.
“Georgia” - Elton John
“Massachusetts” by the Bee Gees.
“Roadrunner” by Jonathan Richman and the Modern Lovers.
You go, Brad! WOO HOO!
Shying away from country songs as I don’t feel like staying up all night making a list, I can safely say “Tennessee” by Arrested Development fits the bill.
“Alabama Song”
“Alabama Getaway”
“Stars Fell On Alabama”
A couple of freebies to help out the other states:
“T for Texas”
“Waltz across Texas”
“Texas Uphere Tennessee”
“Georgia On A Fast Train”
“A Rainy Night In Georgia”
“The Night The Lights Went Out In Georgia”
Carolina Girls. Best in the world. You’re so fine, girl you’re one of a kind. Sweet Carolina girls.
That could be NC, but I doubt it 
Most of mine pertain to the city, not the state, but since I’m from that city it still fits:
New York, New York - the old classic song
New York, New York - Ryan Adams
New York State of Mind
New York - Sex Pistols
There’s most likely a billion more, but that’s all I can think of. Oh, and I Love NY but I think that is the state song, so it doesn’t count. (Reminds me of how as a kid they’d have all these commercials for how great NY state was and they’d play that song and show the “I love NY” logo as with a heart for love…that’s all I see in my head when I hear that phrase.)
There are many songs that mention Japan, I’m sure, but where I live is US territory. There are no songs that mention the name of where I live, but I’ll make one up and call it “Smells Like Yokota Spirit”. : )
“Oklahoma” The entire musical.
“24 Hours from Tulsa” Gene Pitney has a lot to answer for.
The above are so well known, when I moved to England I went through a stage of telling people I was from Minnesota so that they wouldn’t burst into song when I walked into the pub. Nobody I knew then was familiar with any songs featuring Minnesota.
Also, various CW songs give Oklahoma a mention.
California Dreaming
(wish they all could beat) California Girls
The ONLY one that I can think of (even googling), is “Indiana Wants Me,” by R. Dean Taylor
Chiming in with more California songs, two of my favorites…
“California”–Semisonic
“Just Like California”–Old 97’s