I like rivals who present a challenge, both physically and mentally to my character. Personality wise, somewhere between Wesker (Resident evil) and revolver ocelot (Metal gear solid). My ideal rival is sure of them selves possibly to the point of being a self lover or haveing a god complex yet respects my character for what they can do, possibly even come to consider my character a closer "friend" than any other. For me to care about my enemies the relationship has to be fairly deep not just " I don't like you/your stoping me from doing a thing, I'm going to try to murder you". However this only applies if I am on what can be called the good side.
If my character is "evil" then my enemies need to be resolute and firmly believe what they are doing is right. No wishy-washy, overly angsty, constantly self doubting and second guessing whiners. However again I prefer it when my rivals/enemies respect my character, they oppose what I am doing but they wish there were some other option to fighting me.
Anyway I feel like I'm gonna start rambling soon so that's that.