Most of the characters I like fall into multiple good categories for me. For instance, my favorites are Madara, Obito, Naruto and Sasuke.
I love the power and battles of all 4 of these characters (especially the Uchihas).
However, I also have deep respect and admiration for their resolves to obtain peace (in various ways).
Ever since we first saw it casted, I have always thought that the infinite tsukuyomi would be a brilliant way to bring about peace (if it wasn't for the white zetsu, and the stealing chakara aspect). For this reason, and for the fact that I agree with Madara's and Obito's ideology and world view, I have long since regarded both Madara and Obito as heros. They aren't perfect heros, but they're heros nonetheless.
I have seen Sasuke in a similar light ever since his "revolution" phase. I don't exactly agree with all of the aspects of his plan from back then, but the overall principal of revolutionizing the world is a goal I can respect. I also like how shinden and adult Sasuke are so much more mature and diligent in protecting the world.
I've always liked Naruto's resolve. I admit that it's a bit idealistic, but it is the closest ideology to a pacifist ideology. Plus, I like friendly people in general much better than rude, arrogant, and edgy people. Naruto truly cares for people. That is what I like.
Outside of these 4, I also generally like characters who I find to be kind, free spirited, rational or entertaining, even if they aren't the strongest or most revolutionary.
Shikamaru, Kakashi and Hinata are prime examples of this. I greatly admire the rationality/intellectual ability of the former two alongside their lack of arrogance and rudeness. They don't have that superiority complex that I despise.
As for Hinata, I like her kindness and her consideration for everyone (much like Rin and Sarada, both of whom I also like). Hinata was a nice contrast to a number of her female peers in that she lacked that stupid superficiality, and she had depth that made me want her to succeed.
As for antagonists who are pure evil, I like it when they are really powerful or just overall effective as villains. Frieza is a prime example of this. He conquered and effectively became the emperor of universe 7, and he's destroyed planet after planet. He's also amazingly powerful. Everything about him just screams "pure evil! Kill him!". It makes for a great villain.
A villain doesn't necessarily have to be crazy strong to be good though. For example, Plankton from Spongebob isn't really strong, but in the Spongebob movie, his cunning tactics made him very effective as a villain. He pretty much had it won. It was a random rock concert out of nowhere that took him down (and this was the biggest deus ex machina I have ever seen).
