First up: Chihiro.
She is the main hero in this story, a young girl who at first is a crybaby, but as she goes through the many hardships from working at the bathhouse to having her parents turn into pigs, she grows into a mature young lady.
Chihiro, at the beginning of the movie, is very whiny. She's also very dependent on her parents for everything. But when her father decides to take a "short cut" to their new house through the woods, they come across what looks to be an old train station.
As they walk through to the other side, they discover a large open field that they didn't know existed. The dad smells food and decides to go across the river (which is where the magical world lives) and the parents eventually get turned into pigs when they decide to eat the food. Chihiro seems to be the only smart one, though, as she doesn't eat the food at all.
She's scared, of course, and she has help from Haku, a "henchman" for the witch that manages the bathhouse. With the help of Haku and others, Chihiro is then able to get into the bathhouse and get a job. Her name gets taken away by Yubaba, the bathhouse witch, but Haku has her hold onto her name from a card a friend had given her before she moved.
So, at the beginning of the movie, I feel like Chihiro will never grow up, that she'll just be stuck in that world forever, but as the movie plays on I start to really see a development in her that I don't even know where it started. She has manners, she does good work (even if she's slow at first), and she tries to help out as many people as possible.
Toward the end I have a real liking for Chihiro. She grows up immensely and isn't afraid of anything. She's willing to risk it all to save her parents, Haku, and No Face (a spirit) in different instances. All of this can happen from a little girl like Chihiro. It's truly amazing.
Next up: Haku
Haku is a very complex character, I think, in the movie. He first appears after Chihiro wanders from her parents when they're stuffing their faces and she sees the bathhouse and she goes onto the bridge leading to the bathhouse. He's shocked that she's there (everyone from the world that see Chihiro knows she's a human) and tells her to leave. But as night falls, he has to help her out. When she can't get back across the river, he gives her food so she wouldn't disappear from the world and helps her to escape and get a job.
Haku also runs a lot of the "errands" for Yubaba. He's sort of the henchman, but he's also a good guy. It's a hard situation to figure out at first when he treats Chihiro coldly, but he ends up being a really good guy.
Later on, you also find out he's a dragon.
As Chihiro and Haku (as well as Yubaba's bird-turned-mini-bird and son-turned-rat) leave Zeniba's place, Chihiro remembers when she was a little girl how she fell into the Kohaku River and was saved by Haku himself! He hadn't remembered his true identity until then, and they both cry because they were so happy.
And yes, I totally ship them.
Next: Yubaba.
Now, Yubaba isn't very likable from the start. She's a witch that runs the bathhouse and is very cruel indeed. She has a very strong magic, and a baby she loves to death, but otherwise she's not very likable. Her twin sister, Zeniba, is much more likable (which is astonishing considering they look the same but have such different personalities). I don't have much to say about her other than she doesn't develop much as a character and she's really mean.
Next: No Face
No Face is a spirit that has, well, no face, and there is a lot of mystery that surrounds him. He ends up being, what I think to be, a greed spirit that tries to draw others in by duplicating things that they want (such as gold or bathhouse tokens). He turns into a monster when he devours three of the workers from the bathhouse, as well as a lot of food that the workers provide because he gives out "gold" by the handfuls.
Chihiro is the only one that can really save him, and he ends up going back to his normal self. He travels with Chihiro to Zeniba's and ends up staying there as her assistant. There isn't much to say of him other than he's a secondary main character, but very loveable toward the end because he's a misunderstood being.
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So, those are just some of the main characters that reside in the world of Spirited Away. They're all very different and very complex in their own way, but they're still loveable (except Yubaba, but I'll leave that to you to decide).