Super-short guitar solos that are perfect for the song ...

[Mister Freeze]

Kiss happens to have three of 'em...

"I Was Made For Lovin' You"

"I Love It Loud"

"Crazy, Crazy Nights"

Sometimes less really is more.

[HueyRamone]

Heading out to the Highway

[Zabooka]

DEF LEPPARD - "Lets Get Rocked"

[diablomozart]

any cars tune...elliot easton was the master of the cool, succinct, perfect solo...d.m.

[BernieTaupson]

All You Need Is Love

[Hellsinkey]

Therapy- Nowhere

[aznsquirt]

I'm drawing a blank on several, but:

VH - Jump
Hendrix - Fire
Weezer - Say it ain't so (may be too long for this category)

[BernieTaupson]

Jump and Crazy Crazy Nights aren’t short solos.

[aznsquirt]

Jump and Crazy Crazy Nights aren’t short solos.

At 13 seconds Jump sure feels short But maybe it's the 30 plus second keyboard so that makes it feel short.

[Bono Nettencourt]

Everything About You. My friend called it the "Poison solo". It's garbage, but it works somehow.

Speaking of Poison solos, Every Rose fits here too. Simple and fits the vibe well.

[Young Malcolm]

AC/DC-"Shoot to Thrill"

[dmbrocker]

Pop ballads and AOR ballads (and even a few hair ballads) are notorious for these: Sweet Sensation's "If Wishes Came True", REO's "Keep on Loving You" and "Can't Fight This Feeling", Firehouse's "Love of a Lifetime", "When I See You Smile", etc.

[sirthx2]

Livin' After Midnight

[kingrolfus]

Led Zeppelin - Celebration Day

[GreatWhiteSnake]

Man in the Box...

[DangerZone]

Van Halen - Unchained

[Gibsonite]

Perry's first solo in Walk This Way

[tooth]

any cars tune...elliot easton was the master of the cool, succinct, perfect solo...d.m.

This is the answer.
Not sure if they are "short" in this context, but Alex Lifeson certainly made the most of his spots on many of the solos on Signals -> Test for Echo

[Nightcrawler]

Cheap Trick - Oh Candy

[HoldenSSV]

Feels Like the First Time. It's fun to play, too.

[dmbrocker]

Here's a good example of a song with a short solo that works perfectly for the song:

The Night Flight Orchestra - "I Will Try"

https://www.youtube.com/watch?v=MHLQO5iNgQ0

[SchenkerFan]

Rosanna

[sunshinehead]

She Sells Sanctuary
Day Tripper

[dmbrocker]

Rosanna

This one is kind of debatable as to whether or not it counts, though, since there’s a whole keyboard solo just before it.

[pieceofme]

Motley crue girls girls girls. The solo at the end of the song

[WentEast]

AC/DC-"Shoot to Thrill"

Seconded. I learned it a few weeks ago and couldn’t believe how little there was to it but it works.

[kanister]

Kiss happens to have three of 'em...

"I Was Made For Lovin' You"

"I Love It Loud"

"Crazy, Crazy Nights"

Sometimes less really is more.

You Love Me To Hate You has a very tasty short solo too.

[Gwrexx]

“Sabotage” - Beastie Boys

[Mister Freeze]

Kiss happens to have three of 'em...

"I Was Made For Lovin' You"

"I Love It Loud"

"Crazy, Crazy Nights"

Sometimes less really is more.

You Love Me To Hate You has a very tasty short solo too.

That song should've also been the single after "Forever."

[BernieTaupson]

They would have had to record it properly for that, the album version is a touched up demo. Sonically it sounds like it was recorded through a door.

Coming back to topic :

Go Your Own Way solo.