Since Brother Lawoot beat me to The Needle and the Damage Done (nice goin. bro!), I’ll resort fo some of the FZ that Biffy passed over…
Mother People 2:26
Harry You’re a Beast PLUS What’s the Ugliest Part of Your Body clock in at a combined 2:24
Pygmy Twylyte 2:13
The Dog Breath Variations 1:48
Misirlou (Pulp Fiction Theme) 2:30 Dick Dale & His Del-Tones
O Fortuna from Carmina Burana 2:30 Orff
In the Hall of the Mountain King 2:27 Edvard Grieg
Sabre Dance from Gayaneh 2:20 Khachaturian [Plate Spinning Song]
(I just wanna be) Free 2:16 Chicago
Everybody I Love You 2:22 Crosby, Stills, Nash & Young
Hawaii Five-O - Ventures (1:54)
Big Yellow Taxi - Joni Mitchel (2:14)
Do Wah Diddy Diddy Do - Manfred Mann (2:22)
Go Where You Wanna Go - Mamas and Papas (2:30)
Roll Over Beethoven - Chuck Berry (2:25)
Kicks - Paul Revere and the Raiders (2:25)
Fly Me to the Moon - Frank Sinatra (2:30)
Add another ten seconds for
Gloria (the Shadows version, I don’t know how long Van Morrisson’s is)
I Walk the Line AND Ring of Fire – Johnny Cash
No need to guess. It’s listed in the OP as running 2:18. 
I just heard two Offspring songs that I just love…short and sweet (with added bitterness!):
All I Want - 1:54
Staring at the Sun - 2:13
I swear these two songs sound alot longer than the listed times.
White Rabbit - Jefferson Airplane 2:30
2:38 for Gloria by Them (Van Morrison’s band) released in 1964, although his live version stretched to over four minutes. I googled it, of course, but I figured it’d be appropriate for me to submit the information. Alas, Brown Eyed Girl clocks in at just over three minutes.
The Doors:
2:30 Break On Through (to the Other Side)
2:13 People Are Strange
2:16 Hello, I Love You
…and a few other lesser known songs, if you’re really serious about The Doors.
I gotta go for the most copied - Happy Birthday to You
:smack: Couldn’t have been any more obvious, could it? 
2:06 La Bamba - Ritchie Valens
2:07 Papa’s Got a Brand New Bag - James Brown
2:10 Tijuana Taxi - Herb Alpert & the Tijuana Brass
2:12 Purple People Eater - Sheb Wooley
2:16 What a Wonderful World - Louis Armstrong
2:23 What a Wonderful World - Joey Ramone
2:20 Rock N Roll High School - The Ramones
2:21 The Green Hornet Theme - Al Hirt
I think that before the late '60s most songs were under 2:30. For example, yet more early or early-ish great Beatles songs:
“For No One” (2:01)
“I Feel Fine” (2:18)
“If I Fell” (2:17)
“I’ll Be Back” (2:20)
“I’ll Follow the Sun” (1:48)
“In My Life” (2:26)
and many, many more, as they say.
Or my favourite song ever, Jerome Kern/Dorothy Field’s “The Way You Look Tonight” from 1936. Less than two minutes long, that one.
More oldies (time from my iTunes list):
*
Love Potion No. 9* - The Drifters (2:03)
Ain’t No Sunshine - Bill Withers (2:03)
It’s Not Unusual - Tom Jones (2:05)
Sweeter Than You - Ricky Nelson (2:08)
I Only Have Eyes for You - Rosemary Clooney (2:12)
Tequila - The Ventures (2:13)
Needles and Pins - The Searchers (2:14)
You Really Got Me - The Kinks (2:15)
Secret Agent Man - Johnny Rivers (2:16)
Bad Moon Rising - Creedence Clearwater Revival (2:19)
Son of a Preacher Man - Etta James (2:25)
Traveling Man - Ricky Nelson (2:25)
Time in a Bottle - Jim Croce (2:27)
King of the Road - Roger Miller (2:28)
With another 10 seconds:
Mr Tambourine Man - The Byrds (2:32)
On the Road Again - Willie Nelson (2:33)
I Go Walking After Midnight - Patsy Cline (2:33)
Perhaps Perhaps Perhaps - Doris Day (2:34)
Ring of Fire - Johnny Cash (2:34)
Mambo Italiano - Rosemary Clooney (2:34)
Gypsies, Tramps and Thieves - Cher (2:36) (sorry, couldn’t resist!)
The Lion Sleeps Tonight - The Tokens (2:39)
Friday on My Mind - Easybeats (2:40)
Mas Que Nada - Sergion Mendes & Brasil '66 (2:40)
California Girls - David Lee Roth (2:40)
Top THIS:
Teddy Bear Elvis Presley 1:40
Lots of early rock ‘n’ roll qualifies:
Maybe Baby - Buddy Holly 2:05
Everyday - Buddy Holly 2:09
That’ll Be the Day - Buddy Holly 2:27
Bo Diddley - Bo Diddley 1:58
You Never Can Tell - Chuck Berry 2:17
Maybelline - Chuck Berry 2:18
Whole Lotta Shakin’ Goin’ On - Jerry Lee Lewis 2:00
Great Balls of Fire - Jerry Lee Lewis 1:50
Tutti Frutti - Little Richard 2:00
Long Tall Sally - Little Richard 2:10
Bye Bye Love - Everly Brothers 1:25
Love Hurts - Everley Brothers 2:20
All I Have To Do Is Dream - Everley Brothers 2:18
Rock Around the Clock - Bill Haley 2:14
I’m not sure you can count live performances (or youtube clips) as definitive for running time of a song. For instance, the Bo Diddley clip posted appears to be TV show and was apparently trimmed, but the 1958 release clocked in at 2:30. Maybe still applicable by the OP’s qualification, but just barely.
Additionally, (Let Me Be Your) Teddy Bear as released Elvis’ 1957 Loving You album was actually 1:52.
What exactly are the qualifications for shortest songs here? Original releases or any versions?
Thank you for this. This song (WOOHOOO!) has been on my playlist through many revisions/additions/removals. The original release, however, on 1996’s Summer is the Best. Two Minute Twenty-Six Second. Song. Ever. 
Sloan - The Good in Everyone is 2:17 of perfection.
Sneaky Feelings by Elvis Costello, at 2:12, about having a crush on a married person.
These great lyrics
“white lies, alibis, anything but say that it’s true
we could sit like lovers staring in each other’s eyes
but the magic of the moment might become too much for you”
combined with the most impeccably timed phrasing.
Several of those “live” performances are actually lip-synchs to the singles.