There’s a great deal of the punk genre that would fall into the requirements of the OP. Almost too much to mention. Some classic punk releases (the Misfits and the Germs come to mind) have albums that clock in under 20 minutes total.
**Quixotic **beat me to it with the Zeppelin mention.
Nothing else for me to add.
Might have a winner here.
But let’s also consider The Dickies’ Give It Back (1:42)
Re The Beatles - I have 101 of their songs on my iPod that are less than 2:30
Among the best of them: All My Loving, Any Time At All, Can’t Buy Me Love, Do You Want To Know A Secret, Drive My Car, Golden Slumbers, Good Day Sunshine, Help, I’ll Follow The Sun, I’m Happy Just To Dance With You, I Me Mine, I Wanna Be Your Man, I Want To Hold Your Hand, In My Life, Lady Madonna, Paperback Writer, Sgt. Pepper’s Lonely Hearts Club Band, Taste Of Honey.
The dB’s: “Big Brown Eyes” (1:58) and “Ask for Jill,” “Storm Warning,” and “pH Factor” all at 2:30.
The Feelies: “Fa Ce-La” (2:01)
fIREHOSE: about half of their songs overall clock in that fast, but I like their first album best, with “Honey, Please” (2:20), “Windmilling” (2:17) and “In Memory of Elizabeth Cotton” (2:14). Also their “What Gets Heard” (2:20 LP; 2:12 live), and lots, lots more. And for yet more, see The Minutemen.
The Pretenders: “The Phone Call” (2:27)
The Specials: “Do the Dog” (2:09), “(Dawning of a) New Era” (2:24), and “Too Much Too Young” (2:16).
XTC: the LP version of “This is Pop” is a languourous 2:38, but I found a live version that’s a hyper 2:15. Also: “Limelight” (2:25) and “Red Brick Dream” (1:57) are among their better short tracks.
XTC as The Dukes of Stratosphear: “Bike Ride to the Moon” (2:24), “Vanishing Girl” (2:30) and “The Affiliated” (2:17).
Under 1 minute:
The White Stripes, “Little Room” (:50)
The Who, “Medac” (:57)
Moby Grape, “Naked If I Want To” (:58)
Magnetic Fields, “Boa Constrictor” & “How Fucking Romantic” (:59)
Under 1:30:
Big Star: “ST 100/6” (1:02) & “Morpha Too” (1:28)
Guided By Voices, “Kicker Of Elves” (1:06) & “Shocker in Gloomtown” (1:26)
Scott Walker, “Cowbells Shakin’” (1:06)
The Figgs, "Step Back Let’s Go Pop: (1:11)
The Replacements, “Run It” (1:11)
House of Freaks, “This Old Town” (1:17)
Mose Allison, “Young Man Blues” (1:26)
Pixies, "Broken Face (1:30)
dead kennedies - nazi punks fuck off.
I guess it’s a little over a minute or something. Very clear and concise song.
I thought ace of spades (motörhead) was not very long either but it’s actually 2:48. Still quite to the point, though 
Napalm Death: “You Suffer” clocks in at just slightly over 1 second.
True enough that it at least at one time held a Guinness Book record for being the worlds shortest song, but I didn’t mention stuff from the grindcore genre where you have bands like A.C. or Agoraphobic Nosebleed going to extremes to make insanely short bursts of noise and labeling them as songs.
ETA - Warning, both links go to Wiki entries on band albums that contain song titles that are rather offensive to some, so if you’re easily disturbed just trust me on my point.
You can listen to S.O.D.'s Anti-Procrastination Song, Hey Gordy!, Ballad of Jimi Hendrix and Diamonds and Rust (Extended Version) in a total of 23 seconds. If you have time, that is.
Dear Friends from Sheer Heart Attack is 1:09.
The Smiths - Panic (2:18)
Flogging Molly - The Wrong Company (0:35)
Pixies - Allison (1:17)
Pixies - Wave of Mutilation (2:04)
Bad Religion - Stranger Than Fiction (2:20)
I’d be looking up songs all day if I tried to think of everything I like that’s under 2:30, but that’s a little sampling.
Maybe not a hard rockin’ song, but it packs an emotional punch:
“The Needle And The Damage Done” - Neil Young (2:10)
Yup,thats a good one too.
“Harvey the Wonder Hamster” by Weird Al, at 0:21
“Yesterday” and “Blackbird,” too.
I once wrote an actual song with lyrics that had to be precisely one second long. (Title and complete lyrics: “I smell a rat.”) The live recording came out 1.2 seconds, so I sped it up a little.
A personal favorite:
Del Shannon - “Hats Off To Larry” (1:45)
I love the message, which contrasts pretty strongly with other songs of the period. Other songs went, “Okay, you left me, but I still want you back, baby!” This song says, “Okay, I’ll take you back, but first, congratulations to the guy you left me for, for jerkin’ you around the way you jerked me around.”
Marcels - Blue Moon
Castaways - Liar, Liar
Simon & Garfunkel - April Come She Will
Syndicate Of Sound - Little Girl
Yardbirds - Over Under Sideways Down
Jefferson Airplane - Volunteers
Black Sabbath - St Vitus Dance
Buzzcocks - Orgasm Addict
Was (Not Was) - Dad I’m In Jail
John Zorn & Naked City - Batman
Times taken from my mp3 list, YMMV.
Do You Believe in Magic - The Loving Spoonful (2:01)
Girlfriend in a Coma - The Smiths (2:03)
La Bamba - Richie Valens (2:19)
Red Rubber Ball - The Cyrkle (2:20)
No je ne regrette rien - Edith Piaf (2:24)
Skull - Sebadoh (2:24)
What’s My Age Again? - Blink 182 (2:26)
King of the Road - Roger Miller (2:28)
Swinging on a Star - Der Bing (2:29)
Mississippi Queen - Mountain (2:29)
Respect - Aretha (2:29)
I Wanna Be Sedated - The Ramones (2:29)
Allow another ten seconds, and you can add:
Wild Thing - The Troggs (2:37)
Dancin’ in the Streets - Martha and the Vandellas (2:39)
Be My Baby - Ronnie Spector (2:39)
Runaround Sue - Dion and the Belmonts (2:40)
Wipe Out - The Surfaris (2:40)
I Fought the Law - The Clash (2:40) and I’m guessing that the Bobby Fuller Four version isn’t much longer than that
ETA: Just noted the references to “cranking”. This was just put together based on the OP thread title “great songs”. My opinion, of course.
Now you’ve got me thinking (because somehow I missed Švejk’s post). The Dead Kennedys’ version of the song (2:21) definitely fits. So do some other great DK songs: Police Truck (2:27), Winnebago Warrior (2:09), and Well Paid Scientist (2:21).
Elvis Costello - Welcome to the Working Week