The Onimusha series is one of my favourites. Oddly, these sorts of 3D (or pseudo-3D in the case of 1 and 2) action games often have better stories than fully-blown RPGs, or at least more involving stories. I feel the same about the Resident Evil series, Metal Gear Solid series and I'm sure there's a few more games that straddle many genres and seem to have a really great way of telling a story and making you feel involved.
I think my least favourite is the first Onimusha but then I did only play it after I'd played 2 and 3. You could really tell that is was one of those games that was created by Capcom trying to reinvent Resi but moving a little too far away from its roots - that's also how Devil May Cry was created and again, it's most apparent in the first game.
Oni2 is my favourite - I think that game has it all:
[list][*]The best characters (mmm, Oyu...)
[*]The most convincing "fake historical" setting, if you see what I mean
[*]I actually prefer it graphically to 3 and 4, but then I am a sucker for pre-rendered backgrounds in games like Planescape: Torment, the Baldur's Gate series, PS1-era Final Fantasy and Resident Evil 1-3, to name but a few
[*]I really like that for the first half or so of the game, you are based in and around the little village. I don't generally like being pushed through a game in a linear fashion and not being able to return to old levels.
[*]The extras were great and the chart showing you which story paths you had taken really added to the game
[*]I prefer the bosses in Oni2, gameplay-wise and personality-wise
[*]The best replayability[/list:u]
Oni3, in my opinion, only really improved on the combat by making it more varied and more fluid but I still like the Oni2 combat. I really liked how Capcom set it half in France, as well. It's nice to see a game set in a part of the real world that isn't Japan or America (or heavily based on one of the two, e.g. GTA).
Oni4 really did feel like a cheap add-on to the franchise, especially after Capcom repeatedly referred to Onimusha as a trilogy (even on the Oni3 box) and said there wouldn't be another one. Then the 4th comes along and feels so different and cheap. I did get to enjoy it in the end and I like how you can revisit all the areas and get to new parts of them as you gain more characters and their abilities.
I also have Onimusha Blade Warriors which I really like. It's obviously not as good as Brawl or even Power Stone, but since I like the Oni characters more than any Nintendo mascot, I have more fun with playing it.