I'm answering this because I have nothing better to do, and I want Internet points! :D
Pokemon only seen in flashbacks, or Pokemon that were released/traded, still count as being had by a Trainer, for the purpose of this answer. A person that is caring for/protecting a Pokemon does not count as owning that Pokemon (for example, Shaymin was cared for, but never actually captured, so for this list, Shaymin is on here.).
Porygon was never technically under a Trainer's command, just a scientist and even then, only in a banned episode.
Omanyte doesn't seem to have a specific Trainer, according to Bulbapedia.
Kabuto doesn't seem to have a specific Trainer either.
Sunkern (Ash evolved one, but never actually caught it)
Debatably Entei (Illusions of one were created by the character Molly Hale, but it was never technically captured)
Lugia befriended Ash and Goh, but was never captured
Lileep was looked after, but never used by a real Trainer.
Cradily was looked after as well, but never used by a Trainer.
Anorith was never used in battle.
Tirtouga was befriended by someone, but not technically captured.
The same goes for Carracosta.
Archen was revived and raised by Fennel, but never captured or used.
The same with Archeops.
Tyrantrum is owned by Scientists, but never stated to be captured.
Amaura was revived, never captured.
Aurorus was revived, never captured.
Zygarde was captured, but escaped.
Wishiwashis are at the Aether Paradise, they may have not been technically captured.
Palossand is at the Aether Paradise, may not have been captured.
Hope I helped!
Source: Every single Pokemon's Bulbapedia article