That's what gets me addicted to Naruto and Naruto Shippuden! :P

Frankly if all a series has is good characters, I won't always continue watching it. While even if the characters aren't good, if it has a good plot, I'd watch it.

If the main character turns me off, I I won't bother watching/continuing. Then the plot.

If I don't love at least 1 of the characters I won't like a series that much.

Second is humor, third is great villains.

Normally, the characters are my favorite element in the anime. However, if I don't like the general plot, story, and events in the anime, the characters won't be enough for me. For example; I like most of the characters in the Melancholy of Haruhi Suzumiya, but the anime, itself, just isn't for me. I don't like its style, idea, or plot. I can't enjoy it even if I try.

This is more important than like everything else to me.
I'm a total character person. Even if a show has an amazing plot, if I don't like the characters chances are I won't like the show that much as a whole.

a mixture of all actually

Actually, I guess an anime has to have a good plot AND good characters for me to like it. I really like the main character in Mushi-shi, but I get bored of Mushi-shi very quickly because the plot doesn't go anywhere. But I could never watch Bleach, or Pokemon, even though they have interesting plots, because nearly all the characters annoy me. However, I still choose characters over plot; if I don't like the characters, then the battles become dull because I don't care what happens to them... I'm not gripped.

Characters is what keeps me interested, but the plot and twist is also.
That's why Naruto is perfect, mostly during the war and you've watched it since the
beginning getting to see characters that have died and have come back to life, and is able to hear what they have to say like their regrets and mistakes is always touching.
I couldn't ask for a better anime.

I like Fruit's Basket, but im not fond of any of the characters but Kyo

Mix of many of these. But if I don't have a favorite character (and that character is usually evil) than I can't watch the anime.