I’ll add one: The Living End, Second Solution (starts at 1:30). 19 seconds of searing punka-rocka-billy magic, here and then gone again - poof! Definitely worthy IMO, and quite fun.
PS: how do you do that thing where you link directly to specific time in a YouTube video? Someone in this thread did that; that’s pretty cool and I don’t quite see how to do that looking at YouTube’s site. Please clue me.
Oh, I get it! pulykamell did this in post #5. The url he linked to had “#t=90” at the end, i.e. 90 seconds. I tried this in other YouTube links and it works great, e.g. here’s a direct link that takes you right to that Living End solo I posted about. Damned if I know how someone would figure this out without an example URL. 
You can also do “&t=2m45s”, meaning 2 minutes 45 seconds into a video.
Lots of great solos mentioned; love Taxman and Driven To Tears.
Here’s a few that popped up in my mind:
Beatles: Old Brown Shoe - 14 seconds (possibly George’s most fluid guitar virtuoso moment as a Beatle)
Television: See No Evil - 27 seconds (I prefer Richard Lloyd’s flashy solos)
XTC: Are You Receiving Me? 11 seconds (Andy Partridge is a very underrated player. Who knew he could play a mean lead?)
King Crimson: Elephant Talk 33 seconds (Great tidy Belew solo, a little long but with many silences between phrases)
David Bowie: Red Sails 13 seconds (great untidy nearly atonal Belew)
David Bowie: Look Back In Anger 30 seconds (same album as above, great Carlos Alomar solo)
Beatles: Helter Skelter 12 seconds (you’d expect a crazy solo for this song and instead get a short ‘calm in the eye of the storm’ solo)
I can see why folks don’t use this feature much. For me it seems to work about 3 in 5 times I click a Youtube link with an embedded time in it.
I’ve never had an issue with it, myself. Another way of linking to the time is right click the video at the point you want the link at, and one of the options that pops up should be “copy video URL at current time.”
Yep - the slop in Page’s Whole Lotta Love solo is the equivalent of Merry Clayton’s voice breaking when she is belting the Rape, Murder break in Gimme Shelter - only adds to the emotion and power as they try to keep it together and don’t quite succeed.
ETA: I hate thread-shitting, and really try to avoid it, and understand when folks dismiss threadshitters, even when they have something to say. I just struggle with the inclusion of anything by Big Brother and the Holding Company - I am a San Franciscan and Northern California boy down to my bones, but man, they were mediocre musicians at best - easy to see why Janis moved on. Sorry, JKellyMap.
I just have to mention a three-second guitar fill by Robrt Fripp at 3:12 of King Crimson’s “Indoor Games” that cracks me up every time I hear it. Maybe you have to understand Fripp in order to get it… he’s such a precise player, and for the purposes of this song, he inserts this intentionally horrible bit.
For a more representative sample of Fripp, I submit the solo from 1:21 to 1:51 in Brian Eno’s “St. Elmo’s Fire”.
Well, the topic is favorite ultra ultra short guitar solos, not best. There are no wrong answers. 
And I kinda like that opening. It’s rough, but around 0:15 it starts that downscale then upscale then downscale set of riffs as Janice comes in that works pretty well for me. I’m really not fond of the rest of the song, but that part’s okay IMO.
If I repeatedly click the link I made above (this one) I often get behavior where the video loads but doesn’t seek to 90 seconds like it should, it just plays from the start. Not every time, and it seems once it behaves properly it will do so on subsequent clicks for a while. I’m using Chrome.
Aha! Exactly what I was looking for. Thanks!!
TR’s solo in “I saw the light” probably one of the first examples of harmony guitar leads and one of the great Tom Scholz’ (Boston) top 10 fav’s:D
Is 37 seconds too long?
If not, here’s a blast from the past - SRC doing The Angel Song (from their 1969 album Milestones). The solo I’m talking about is from 3:48 to 4:25 (and, if you’re interested, there’s a longer one starting at 0:45 and going to 2:00).
The only link I could readily get is THIS ONE from Grooveshark. Just click on The Angel Song link.
Frenetic six second guitar solo starts @ 1:40. 
Nels Cline in the live version of Wilco’s The Late Greats
(1:36-1:48)
Ramones, I Wanna Be Sedated
(0:56-1:07)
Beatles - Long Tall sally (2nd solo)
(1:07-1:23)
Chuck Berry - Maybelline
(1:05-1:28)
I don’t really consider solos over 20 seconds as that ‘short’, but it’s arguably the original guitar solo.
Green Day - When I Come Around
(2:12-2:22)
Strokes - Last Nite
(1:59-2:13 (arguably))
Two.
First, the acoustic guitar intro at the beginning of Heart’s Crazy on you
Second, the guitar solo in Sultan’s of Swing.
I’d like to learn the guitar just to be able to play those two solos
Ha, I like that one, nice!
This too.
And I think that is the third one note solo in this thread. 
We seem to have settled on a limit of 30 seconds in the thread; there’s only been one entry over that limit so far. So yeah, probably. Good solo, though.
Well, it is a solo guitar, but I don’t think that makes it a guitar solo. And it’s a bit long at 37 seconds, our third entry at that length. 
Which one? There are two. And both, especially the second one, are too long for the thread.
Both (or perhaps all three ) are great pieces.