I have to say Mat is in my opinion one of the best characters ever written, alongside Kaladin Stormblessed and Tyrion Lannister (the latter is the clear winner every single time in my opinion, absolutely perfect character).
Rand, I have a huge soft spot for. Perrin I also really love but Faile ruined him for me.
Mat, however is the epitome of the reluctant hero. Never wants to get involved, very verbal about not wanting to be there, or involved, but comes through time and time again. The kind of man who goes back in to the burning building to get the cat out.
In the early books he's a scoundrel, but I think that just adds to his character. He's cracking jokes just minutes before defeating Galad and giving Gwen a concussion. I just love him.