I feel like the first three games in this series were some of the best games of all time, and, while I understand that there is a niche of people who really loved them, they are nowhere near as appreciated as Capcom's other two similar series - Resident Evil and Devil May Cry, both of which survived their first generation. Onimusha has a unique setting in feudal Japan, and the gameplay is the perfect fusion of Resident Evil, with its puzzles, controls, realistic setting, and focus on exploring a few key areas throughout the game, and Devil May Cry, with its upgrade system, stronger focus on action, and more supernatural themes. Out of the first three games, I cannot pick a favorite, because they are all very high quality games, and, if anything, improved with each iteration. Onimusha 4 (Dawn of Dreams) is the odd one out, and I feel like it's not as strong as the original trilogy, but it, too, is one of the better games in the PS2's library, has the best soundtrack in the series, and is a very fun game to play in co-op.
It really is a huge shame that this franchise never lived beyond its first generation - it was born and died on the PS2. Worse yet, the pre-rendered backgrounds make an HD remaster unlikely, even with the recent influx of HD-ified games. An Onimusha on PS4 seems like a pipe dream - especially since the series left off on somewhat of an odd note - but the dream is definitely still alive in the hearts of the series' fans.
Oh, and it's most definitely not alive in whatever that mobile card game... thing that was released is. That's hardly Onimusha.