Star Wars The Original Trilogy, Definite Collection is close to the original theatrical release, some changes exist, but no many. See
Star Wars Episode I: The Phantom Menace, Theatrical Version in LD Only
THX 1138, Original Theatrical Version on LD
Scream, NC-17 cut only on LD
The Alamo - Director's Cut on LD
It's A Mad, Mad, Mad, World
Fierce Creatures - still haven't released a widescreen DVD of that in Region 1 yet
Beauty and the Beast (Disney) - only widescreen version of the movie in the proper aspect ratio of 1.66:1. DVD and Blu-ray releases were 1.85:1 and 1.78:1. LD is also in the original color scheme, not the retouched version from 2001.
Lady and the Tramp (full screen) - only way to get the Academy Ratio version of the movie. Full screen versions on DVD are cropped/P&S
One Million Years BC - DVD is missing some footage
Return of the Living Dead I and II - have the original soundtrack, DVDs have different music
The Gate to The Minds Eye - Latter LD release has DTS soundtrack not available on DVD. Video is also superior to DVD.
Akira - Criterion CAV Edition. Presented in original color scheme and original English dub (by Streamline) is included.
The Devil's Advocate - Contains "Ex Nihilo" sculpture and original soundtrack that were removed in latter DVD releases due to copyright reasons. It may not be anamorphic and have lower bitrate AC3, but the Dolby Surround PCM track is still kicking!
Blank Check - Unlike the region 1 DVD release, this is in widescreen.
The Lion King - Original 1994 theatrical cut and 5.1 Dolby Digital mix. Latter releases on DVD and Blu-ray are the retouched 2002 IMAX and 2011 3D versions.
Toy Story Deluxe CAV LaserDisc Edition (contains politically incorrect version of short "Knickknack")
Who Framed Roger Rabbit Has the risque Scenes
Betty Boop: the Definitive Collection vol. 1 & 2, Not on region 1/A DVD/BD
The Compleat Tex Avery, Not on region 1/A DVD/BD
Happy Harmonies (MGM cartoons), Not on region 1/A DVD/BD
Olympia, Not on region 1/A DVD/BD
Song of the South, Not on region 1/A DVD/BD
Last of the Mohicans Theatrical Cut on LD, different cuts on DVD/BD
Damnation Alley , Only on PAL LD
Kådisbellan (aka. The Slingshot), OAR on LD only
Ghost Town, not on DVD

Tons of horror and anime

The Alamo - Directors (now deteriorating, will be gone before someone restores it)
It's A Mad, Mad, Mad, World

Fierce Creatures - still haven't released a widescreen DVD of that in Region 1 yet
Beauty and the Beast (Disney) - only widescreen version of the movie in the proper aspect ratio of 1.66:1. DVD and Blu-ray releases were 1.85:1 and 1.78:1. LD is also in the original color scheme, not the retouched version from 2001.
Lady and the Tramp (full screen) - only way to get the Academy Ratio version of the movie. Full screen versions on DVD are cropped/P&S
One Million Years BC - DVD is missing some footage
Return of the Living Dead I and II - have the original soundtrack, DVDs have different music

That's what I can think of off the top of my head

I'm very interested about those Return of the Living Dead movies.

The Gate to The Minds Eye - Latter LD release has DTS soundtrack not available on DVD. Video is also superior to DVD.
Akira - Criterion CAV Edition. Presented in original color scheme and original English dub (by Streamline) is included.
The Devil's Advocate - Contains "Ex Nihilo" sculpture and original soundtrack that were removed in latter DVD releases due to copyright reasons. It may not be anamorphic and have lower bitrate AC3, but the Dolby Surround PCM track is still kicking!
All the Star Wars movies released on LD. They all have cuts that differ from the DVD and Blu-ray releases, even Phantom Menace.
Blank Check - Unlike the region 1 DVD release, this is in widescreen.
The Lion King - Original 1994 theatrical cut and 5.1 Dolby Digital mix. Latter releases on DVD and Blu-ray are the retouched 2002 IMAX and 2011 3D versions.

All I can think of now.

I could rattle off a tonne of music LDs which look and sound better than the re-issued DVDs.
All Roxette LDs are vastly superior to the horrible compressed DVDs that were issued.
Chaka Khan live at the Roxy from 1981 - original Japanese LD is superb compared to truncated, grainy footage on Australian DVD - looks like it was made by a few students drinking beer!

Kylie - Live! (1992) - the recently released dvd is on inferior quality (looks vhs sourced) and is also missing songs and behind the scenes footage. Even the cd release is of inferior audio quality.

Isn't The Princess Bride Criterion the only way to get it with the proper aspect ratio as well?

The original STAR WARS trilogy is only the first edition NTSC laserdisc versions as the CAV THX versions are not the originals!

There is dialogue panning that has been removed in Return of the Jedi on CAV THX and so on though the list into DVD and yes the so called perfect format that THINKS its better than Laserdisc.
I’m after first edition STAR WARS letterbox NTSC USA and The Empire Strikes Back letterbox NTSC USA I have Jedi and CAV and CLV THX editions sigh the DOLBY mix why did Skywalker sound had to mess a good thing up! That studio has lost my respect its now a junk crap Skycrapwalker Sound owned by that Lucas and he can keep his STAR WARS bluray HD crap now!

Most Anime is better on LD. Believe it or not. Most music discs are as well. I agree with the person that said it looked like someone taking a vhs copy, peeing on it, soaking it in acid, putting it in the sun and then copying it 10 times and using the 10th copy to make a DVD.

For me, I really appreciate the LD copy of The Truman Show over the special edition DVD release. Aspect ratio, colour and sound all appear better to me on the LD.

I understand that there are some really good Japanese anime DVDs, but I've not seen them ; of course, they're region-locked. American anime DVDs tend to be overcompressed, & for older material are often as not taken from composite sources anyway. It's a major reason I never bothered with DVD.

Anime looks awesome on Laserdisc. There is definitely some hit and miss on DVD. But (and I know its not the forum for it) Anime on blu-ray looks absolute beautiful. Some of the new One Piece stuff looks sooo good but my favorite is Paprika (sadly not on LD). The colors in that movie are astonishing .

Not on (region 1) DVD/BD:
Betty Boop: the Definitive Collection vol. 1 & 2
The Compleat Tex Avery
Happy Harmonies (MGM cartoons)
Olympia
Song of the South

Unedited/original theatrical version:
Star Wars trilogy
THX-1138
Toy Story Deluxe CAV LaserDisc Edition (contains politically incorrect version of short "Knickknack")
Who Framed Roger Rabbit

Better extras/commentary tracks:
Crash (1996, Criterion)
Midnight Cowboy (Criterion)
Monty Python and the Holy Grail (Criterion)
Scaramouche (Criterion)
They Shoot Horses, Don't They? Boxset
This is Spinal Tap (Criterion)

You said Roger Rabbit, ehehehehehe. There are a ton of Laserdiscs not on DVD
Highway to hell
Transformations
Horror Planet.

Most horror movies from the 80s and 90s, lol

How about Last of the Mohicans (1992)? The Laserdisc was the original theatrical version while the DVD was the inferior (IMHO) Director's Expanded Edition. I was hoping with the Blu-Ray we'd get another chance at the original version but nope, Mann went back and created a whole new version again.

Isn't Horror Planet on DVD under the title "Inseminoid"?

Gotta mention Damnation Alley (AGAIN!)
It was only issued on LaserDisc in PAL, still a great score all the same !
Officially issued on VHS......
Bootleg DVD's are out there however the quality of picture / aspect ratio leaves much to be desired....
Not to mention sound.

The original Streamline dub is actually available on Dvd in Europe, although it's Pan&Scan and seems to be a rip from a VHS-copy.

Kådisbellan (aka. The Slingshot) is in its original aspect ratio on Laserdisc (1.66:1) but Pan&Scan on the Dvd.
Does anyone know if Ghost Town has been released on Dvd?

Not to my knowledge. Which is why I just bought the LD of the movie off of Ebay.

As far as anime on LD, when it comes to localization on DVD here in the US, it really depends on what they used for the master. The original US DVD releases of Cowboy Bebop were obviously using an LD as the master since there was a lot of recorded-in cross color artifacting (which wouldn't go away even through a component or RGB connection.) Same goes for CPM's release of Iria.

Another title I had to import the LD of because of the US DVD looked like crap was the ADV release of Variable Geo. They must have used a tape master for that because it was just ugly.

For other dubs not available on DVD, there's the first four volumes of Giant Robo released by Pioneer on LD. Those have the LA Hero/US Renditions/Manga Entertainment dubs. AnimeWorks re-released the title on DVD, but made their own dub.

But, there were only 4 LDs of the series released in the US.