Howl's Moving Castle is my personal favorite. Also one of the rare cases where the English dub is on par with the original voice-acting. English cast includes Christian Bale, Jean Simmons and Billy Crystal.
Nausicaa of the Valley of the Wind and Castle in the Sky are the most similar in feeling to Princess Mononoke. High fantasy, adventure, against all odds. (This is my favorite batch of Ghibli / Miyazaki / Takahata films.)
Spirited Away is an otherworldly coming of age treasure that cannot be missed. Totoro and Kiki's Delivery Service feel similar. Whisper of the Heart is this too, just aimed a little older. (And if you like that, check out Your Name by Shinkai or Wolf Children by Hosoda - not Ghibli films, but very deserving of a watch if you like this sort of film.)
Grave of the Fireflies is a very poignant anti-war film.
FWIW, I bought the old Miramax domain name for Princess Mononoke and kept the website online [1]. It's one of my favorite films. I wish Miyazaki made more films like Mononoke and Nausicaa - they're sublime.
On a more serious note, the book is quite good too. The book doesn't describe the castle as a giant steampunk thing walking around in the hills. It's actually just a plain 4 sided stone building that hovers around a little over the ground, no legs. So in this regard the movie is better IMHO. But in the book there is another location the door opens to and the stuff we see in there changes the whole story. In the movie we spend some time trying to figure out what version of the characters, Howl especially, are the real version. The book turns this up further with the additional location.
At the end the take away is quite different between book and movie. Both good in their own ways.
I love the ending