Single week spent sniffing through various lists and shops and wherever, 'twas tiring but manageable - this is a semi-final listing (too bad I was unable to find any kind of an official SONY catalogue number master list like there is for PlayStation games, nor the fabled more complete database some user on LDDb forgot where it was) of titles released exclusively on UMD Video and unfortunately nowhere else, presented here by yours truly
Info: UMD Video (& UMD Music + UMD Music Video; both with no exclusives) is a home video distribution physical media format by SONY for the PSP (exclusively; no other players ever materialized) - only NTSC 480i h264+ATRAC, usually with subpar results and extras removed, very inferior to DVD (except for having capabilities almost like BD-J, dunno of much else though), and would've loaded atrociously depending on compression levels used; in the end both the media and this format didn't perform well (technically speaking) and it all got phased out with PSP Go
JPCSP can emulate it (but with subpar results due to emu's buggy nature), while PPSSPP disables that function having no code to work with the format (devs themselves expressed no interest in making it happen, noting it's like coding an entire player program like PowerDVD or something along those lines) 
Thankfully videos can be ripped using these utilities (though the latter needs editing batch files to more optimal FFmpeg settings), but unfortunately the interactive (PG) titles still can't be emulated well it seems 
- 7 At One Stroke: UMD Demo by Sony DCE (UMD creation related promo - not much else said)
- AKB1-48 - Idol to Guam to Koishitara (extra UMD; with video content not present in either DVDs nor BDs related to this specific idol worshipping bundle)
- Anime Sampler 1 (German promo disc with trailers - IDK how this ain't bootleg)
- Boku Dake no Kajitsu (surprisingly an exclusive VN)
- Capcom PSP-Lineup Special Collection UMD (promo)
- Devil May Cry 3 Material Archive - Note of Naught (bonus behind-the-scenes exclusive with the book)
- Durarara!! 3way standoff Limited edition bonus -Making of 3way standoff- (bonus disc exclusive with the initial Japanese PSP release)
- FALCOM UMD DEMO COLLECTION 2006 (another Japan exclusive promo)
- Genesis of Aquarion Special UMD VIDEO (purchasable title, part of a promotion related to Super Robot Taisen Z, with goodies related to the animu series)
- Growlanser V - Characters Guide (vintage preorder exclusive of unknown content)
- GUILTY GEAR FRAGMENT (supposedly also a preorder exclusive for JUDGEMENT)
- GUST and NIPPON ICHI Triple Toy Box (collection of extras from games of both poblishers)
- Harukanaru Toki no Naka de 3: Unmei no Labyrinth fandisc - Kinjirareta Tobira (supposedly an episode or something - not a clue)
- Macross Ultimate Frontier - Chou Jikuu Nyan-Nyan Pack (Japanese Limited Edition bonus - maybe wasn't worth pressing AFAIK)
- Screamers, Shockers and Sharpshooters (same as above, this time it's footy)
- State Of Origin Standouts 1991 to 2003 (ditto)
- Sweet Paradise - Saaya, Runa, Jessica to Tropical Date (same as that English bugger above - this time some J-Pop idol group is involved)
- The Legend of Heroes Gagharv Trilogy Special Disc (only ever available mailed to verified owners of all three installments, contents also unknown)
- The Silent Hill Experience (promo - for the movie
) - Tokyo Travel Guide (Hong Kong tourism magazine related - dunno if it's a bonus or something else)
- Toono no Yakata - Chapter 1 [Contract] (NSFW lolicon VN - I warned you
) - Tsugi no Giseisha o Oshirase Shimasu (mail-order bonus disc, or something)
- ULTRA SERIES Shinji Higuchi SELECTION (another one of them compilations, this time of Ultraman stuff - also likely not worth the time)
- Video Commentary! Video & Photo & Music playback on PSP!! (some special interest instructional of unknown content)
- Zettai Meikyuu Grimm Special UMD (more mail-only VN-merch fluff)
- Zettai Shougeki ~Platonic Heart~ (even though it's related to an animu series, this VN is exclusive for reasons unknown; this time played vertically
)
Stuff I haven't included:
-A dozen or two of Japan exclusive pr0n (both JAV and hentai) DX Nugase strip slots and mahjongs and yakyukens and whatnot (some may or may not have been ported to DVD or BD; didn't wanna bother either way, one'd look 'em up on Suruga-Ya if/when desired)
-And some other titles or promos that may have been missed out (some Video titles somehow exist with Game labels on case and caddy and elsewhere for no apparent reason, so that's another doozey)
Forgot why I've went down this rabbit hole to begin with, either way it's finished -
to (maybe) rockleevk for indirectly notifying elsewhere on the interwebs about this format, and to everyone else for, uh, something; either way feel thanked 
UPDATE1: OP fixed a bit + six new JP rarities added
Windows is shutting down
