So many great songs have already been mentioned, but let me add a few more.
Same Auld Lang Syne by Dan Fogelberg, which only gets airplay around Christmas despite the only holiday references being the lyrics in the second line and the sax playing Auld Lang Syne at the end.
Or if funny is more your vein, Sittin’ Up With The Dead, by Ray Stephens.
I could probably give a decent synopsis, but the point of the thing is it is a long and rambling story that really only ties together at the end, so making it shorter kind of ruins it.
I agree with others that you should listen to a recording, as there is much that will not come through on a printed page.
And “lyrics” is probably the wrong word to use. While Arlo plays the guitar throughout, he’s just telling a story (except during the chorus). There’s no particular number of syllables per measure or anything, just “play these chords over and over while you’re talking”.
As others have said, it’s not exactly “anti-war”, although that’s a fair characterization. How about, “It is the (fictional) story of how Arlo Guthrie tried to avoid being drafted into the Army, and how the (mostly true) story of having Thanksgiving dinner with a friend related to that.”
Used to be the Classic Rock station would play it every year on Thanksgiving, at noon. Not many 18 minute songs get that much airplay. 
also appreciated by folkies is the really long and funny in the fashion that his dad, Woody, did so well.
Wildfire by Michael Martin Murphy
Shannon by Henry Gross- I cannot listen to this song without crying.
This may be my longest running thread on SD! Keep 'em coming.
I’ll add Loreena Mckennitt-The Highwayman
Kilkelly, Ireland - but be warned: it’s a sad song and a true story.
This one is one of my favorites – and quite recent to boot!
Jeff Daniels (the actor) has written several story songs. For example, Dirty Harry Blues, about getting shot by Clint Eastwood (in a movie), and Recreational Vehicle, which is actually just a story with guitar accompaniment (like the non-singing portions of “Alice’s Restaurant”).
How about Telegraph Road and 5:15 AM by Dire Straits and Mark Knopfler respectively*. Knopfler seems to be fond of story songs and I think these are both good examples that cover long time periods.
*You could make a fair case that Dire Straits was really not much different from Mark Knopfler with a backing band. . . But that’s another thread.
How about Scott Walker 's ** The Seventh Seal **?
'On the Road to Fairfax County" by the Roches.
Oy! I fell for that one!
It’s a fun rendition, to be sure, but I’ll stand by Springsteen/Seeger.
–G!
Yes, yes, yes!
Oops. Meant to add one of my favorite Stan Rogers’ songs: Witch of the Westmoreland.
I love to sing along in the car … when I’m alone. No one wants to hear me singing.
Jesus - The Missing Years by John Prine.
Not just a story, but the story behind the story.
Funny, good one!!
And now for something completely different…
Taro by Alt-J
The meaning behind the song is here: Taro by Alt-J - Songfacts
I recommend listening the first time with the lyrics on the screen:
There is also a version with a selection of Capra's photographs: I was drawn to this song before I understood what he was singing about; finding out just made me like it more. A grim subject, but for me the song is poetic and beautiful.Can’t believe I didn’t put this into my original post.
Damn near every song Al Stewart has ever written.
For example: Old Admirals is the story of Admiral John Arbuthat Fisher.
Flying Sorcery is the story of Amy Johnson, who was England’s version of Amelia Earhart.
Genie on a Tabletop was written in honor of Ol’ Satchmo - Louis Armstrong.
It’s nice to have people agree with you on matters of taste. I recently bought a copy of No Kinda Dancer purely because I knew it had “Front Porch Song” on it, and I didn’t check the rest of the songs before giving it a listen. When I ran into “The Armadillo Jackal” on side B, I was overjoyed. I knew the song from the radio, but didn’t know I’d bought a copy of it.
Lou Reed’s “Street Hassle” has a humanity that relates in the same way, but brings at least two stories in a direct way that no hunting story can relate to a person who’s lived in a modern metropolitan area. The second story is from the point of view of a shithead, but his perspective is appropriate for that shitty world. The lady he’s talking about is human, but there’s nothing that can be done for her now in their world.
The third movement is an appeal after either of the first stories have passed. It’s just as true as the first two. I only purchased that record in the last few years, but it’s only brought out when I’m ready to be moved to tears.