I REALLY like Surfer Joe And Moe The Sleaze, and I wanted to post it, but abstained because I thought it to be too obscure. Now you’ve forced me ;).
ETA: but if anybody posts something from Landing On Water, the thread will really jump the shark.
Already mentioned as well. I doubt anyone but a fan would have heard “Southern Pacific.” “Sample & Hold” got a little airplay when Re-ac-tor was released, but it vanished quickly.
MidEast Vacation is pretty cool and not often heard.
Trans is one of my top 10 Neil Young albums.
Computer Age
Computer Cowboy (AKA Syscrusher)
The 2 best songs on the album tho are:
In fact, I loved his Geffen years, overall.
Wonderin’ from Everybody’s Rockin’. I’d list more but the album is mostly covers. Fantastic covers, but covers nonetheless.
And even after he left Geffen (finally), he continued his “stylistic” period and tho the album wasn’t a success, there are a number of great tracks on This Notes For You, most notable perhaps is the title track.
Also, I got my girlfriend (at the time) a copy of his live album Arc/Weld when it came out. When we broke up, I took the 35-minute feedback collage Arc. I’ve listened to it hundreds of times. It’s right up there with Lou Reed’s Metal Machine Music and K.K. Null’s Sonicfuck USA as one of the greatest All-Squall™ albums ever. I’ll spare y’all the link, tho. 
But it’s down to a “best” of those which in the case of Neil means reducing from a huge pool of possibles. There are many classics that have no public life at all for even those who can name his greatest hits, or even the songs on Decade.
i’m way more into Neil Young than most people might be though.
Does Albuquerque count as a deep cut? That’s a great one, one of the slowest paced songs I know.
And Barstool Blues, if it’s a deep cut. I’m a Neil freak, so I could go on. I’ll leave it with those 2 for now.
(Ok, Bandit from Greendale. Deep cut?)
((Interstate, too. That one I know is a deep cut)
Probably not deeeeeeep cuts, but two less-often-heard ones I like are Vampire Blues from “On the Beach” and When You Dance from “After the Gold Rush”.
Not attempting to derail, but there is obviously some degree of disagreement over the term deep cut.
I could name at least a half dozen tracks off of Decade that I consider deepish. I know others would think not.
mmm
I’ve always liked the Crazy Horse stuff and I’m counting Year Of The Horse, the whole album, as a deep cut because it’s rarely mentioned outside of NY aficionados.
I dunno, I’ve always thought that this is by far the worst of the three official live albums with Crazy Horse, with Live Rust and Weld being such great forerunners. It sounds even muddier than most NY recordings, and the choice of songs is erratic, but as always with Neil that may be some of the charms of that album.
Yeah, I love it.
The video I linked above is not exactly what I thought it was. More like a live performance from the same time Year Of The Horse was released. I guess there was a documentary of the same name but I haven’t seen it. The YOTH CD that I have was given to me by a co-worker who is a huge NY fan. He didn’t really care for it but knew I loved the Crazy Horse stuff.
Ragged Glory is also one of my most played albums.
Oh yes, definitely. Shows perfectly why Crazy Horse is the greatest garage band of all time.
A status just slightly above being the greatest lawn chair.
(I keed, I keed.)
More seriously, how the hell can any of us know what is a deep cut to a casual fan?
Worth checking out:
20 Insanely Great Neil Young Songs Only Hardcore Fans Know
mmm
I can’t find a version on Youtube that sounds decent, but the 9 minute (or so) Ambulance Blues has been my #1 NY song since I found the record 22 years ago.
The Last Trip to Tulsa, final track of his first album, Neil Young. Settle in for a spell with this 10 minute psychedelic gem
Shakes fist Garage bands are the backbone of rock’n’roll!
Some may understand “Computer Age” better in the Sonic Youth version.
“Like an Inca” is the best out of the Island in the Sun sessions.
Lots of classic Neil motifs in “I’m the Ocean”, from the Pearl Jam record.
“Who took everything from where it once was
and put it where it last was seen?”
I thought they were the 3rd greatest garage band of all time. 
If “Powderfinger” counts I’ll go with that. One of my favorite NY songs.