This is less about what I like about Natsu, and why he's one of my favorite characters, but more about a cool fact that maybe a lot of people overlook. Natsu is of a royal family. Not a very orthodox family, sure, but still a royal family. Natsu, as of the end of the Tartaros Arc, is the king of all fire dragons, extinct though they may be.
If a king has no son at all, he chooses who will take the throne. If a king has no biological son, he has the selection of choosing someone or making an adoption for a son to take his throne after he dies. Igneel found Natsu when Natsu was "a small child", and raised him as a son. Igneel adopted Natsu. The whole time we've known him, Natsu has been the prince of all fire dragons. When Igneel fully passed away (body and spirit), by hierarchical standards, Natsu inherited the metaphorical throne of The Fire Dragon King. Hail King Natsu!