But not all anime movies are based on manga or books, or anything, some just are. They probably shouldn't be discounted on the part of others.
But, not everyone likes what I like, and that is your right.

Sword of the Stranger really didn't feel similar to Ninja Scroll for me, which are both good for different reasons but I like SotS better. Sword of the Stranger kinda felt like epic disney cartoon to me, but a lot more violent.

Have you seen The Girl Who Leapt Through Time or Summer Wars? I have a feeling you'd like those. Maybe not as much with TGWLTT if you need action.

I've been meaning to check out Summer Wars ever since it came out over here, just haven't really gotten around to it. I've heard of The Girl Who Leapt Through Time, but never met anyone who recommended it, I'll look into it. Some reason I always find it harder to find time to watch anime movies than series, even though I rarely ever finish even relatively short series. I think I've seen SotS, FMA: CoS, Castle in the Sky, Steamboy, Akira, Blade of the Phantom Master, Eva 1.11, if FF: Advent Children counts that too, and Gintama: The Movie. Compare that to the several dozens of anime TV series and OVA I've seen.

Here's one that is both an Anime movie and based on a book. It's actually pretty good (imo) and for once is a film that actually follows the book it is based on! < The Disappearance of Haruhi Suzumiya >

Sadly it does appear to be a rare thing when a film based on a book actually follows its source material. T_T

Very true. However, I don't like films in general to begin with. I find that 2 hours are generally hardly enough to provide me with an interesting enough story, so I generally discount movies just from being movies. I'm not over watching a movie based on longer material though, seeing it acted/animated can make it fun (specially if it's action oriented). However, I generally get bored fast and can often get annoyed at the changes, so I tread carefully even then.
Yep, that's a pretty good one. The Hellsing Ultimate OVAs were pretty good too, as far as I saw (never actually bothered watching the whole thing).

Actually, I have a question now that I think about it. A good while ago I saw the end scene to an anime movie where you had a few of the main characters die in mechs underwater. It was supposed to have been a pretty sad movie and the dog died in the end too. Not a lot to go on, but that's all I remember. Any guesses?

I'm still waiting for them to release the final episodes: Hellsing Ultimate 9 & 10. T_T Hopefully one day it'll happen. ^_^

That sounds very familiar... but I can't place it... >_<

In that case I'm going to throw out a recommendation for the anime film: Redline. It's heavily action oriented. -_^ (And more than a little bit off the wall crazy! . . . but in a very good way. ^_^ )

The film Redline is not based on a book to my knowledge though so it may not apply... XD
(Warning to potential viewers: It's not a children's movie due to some mature content, so best pre-watch it before putting it on for the family. -_^ )

I recently got to watch the CG Space Pirate Captain Harlock. That's a pretty good one too.

Since everyone's recommending other movies, a good one is "Kiki's Delivery Service". Though you shouldn't watch it for the end but for the journey and with that I don't mean it has "action adventure" it's more of an usual life of a witch :P, but since I love these kind of movies I enjoyed that one.

Also "Laputa: Castle in the Sky" This is more of an adventure amidst a conflict in a stempunkish place.

And a different one, "Zero Hiki no Goshu" about an orchestra player who improves his music through his encounters with a cast of animals.

Well I may as well add a suggestion to then. Two in fact. Whispers of the Heart and Children who Chase Lost Voices from Deep Below. The later being far more Ghibli-esque than any of Ghibli's own recent releases.

I'm more into the work of Makoto Shinkai and Satoshi Kon than Miyazaki by now, but I still like Ghibli stuff.

My favourites besides Mononoke-hime are
"The place promised in our early days"
"5 centimeters per second"
"Perfect Blue"

My collection is huge and most of it are series rather than movies, but if I have to get down to the best ones these are my choices, because there is a bloody lot going on between the lines.

PS: The soundtrack of Mononoke-hime is by far the best one in my collection. Joe Hisaishi makes awesome stuff.
I played it a few days ago when my gf was there. She never has seen the movie and is very prejudiced regarding Anime, because most Anime stuff that was streamed in German TV was for children and most people here think, that it's stuff for kids because of that.
She partly recognized the scenes only because of the music, although she never has seen them.