If anyone's wondering why I didn't include other characters, it's because I was going by the Disney Princess line mostly. And Hans is a villain, which is why I didn't include him. But since we're talking about them anyway, I'll rank them in parentheses.
By personality, I'd rank them:
(Hercules)
1. Aladdin
(Milo J. Thatch)
2. Li Shang
3. Prince Eric
4. Naveen
5. Kristoff
(Tarzan)
6. The Prince
7. The Beast
8. Prince Charming
9. John Smith
(Phoebus)
10. Flynn
11. Prince Phillip
Aladdin is just so sweet, and I've always loved him. "OJA (Reprise)," his face when he first sees Jasmine in the marketplace, and his interaction with Abu all make him endearing for me, and "A Whole New World" is one of my absolute favorite romantic moments in a Disney film. Brad Kane's voice is just so silky and beautiful. Maybe not my favorite male protagonist overall (that would be between Hercules, Jim Hawkins), but definitely the best of the princes. Shang's grown on me over time; the funny thing is most of what I like about him are his interactions with Mulan while she's pretending to be a man.

I would rank Naveen higher if I didn't think of the characters in a romantic sense (no way would he stick with one person), but the character has the whole intoxicating libertine personality down. Kristoff is probably the prince with a sense of humor/personality most like mine, and I find him sweet and funny in a wry way. The Prince is definitely my favorite of the old princes; the opening where he sings to SW has over time grown into one of my favorite Disney moments.
As for the others, eh. When I'm watching B&tB, I'm rooting for Beast and identify with him, but I don't really think of him as a character I'd want to end up with. He's probably the most developed of the princes as a character, I kind of have a disconnect as far as looking at him in a romantic light. I'm not really a fan of the others, but I do like how Charming is aloof and not interested in romance at all, which kind of makes the way he's attracted to Cinderella more romantic. I find John Smith mostly bland, and Flynn unlikable. My dislike of Phillip is irrational, that's the only reason I can explain putting him below the other two Walt-era princes.
By looks, I'd say: Prince Eric > Aladdin > Naveen > The Beast (Human...just if that wasn't clear, I'm not a furry) > Li Shang > (Tarzan > Milo > Hercules >) Flynn > Prince Phillip > John Smith > The Prince > Kristoff > (Phoebus >) Prince Charming