I also like them on a bacon cheeseburger (Red Robin, yummmm!), in which case they should be done over-hard.
The Royal Red Robin burger is one of my favorites! So good. I always order the egg over hard.
In general I don't like runny yolks. I know salmonella is highly unlikely, but it's all I think about when I see runny eggs. Also, i just don't like the texture of it that much. I like the yolk to be cooked all the way through. Accordingly, hard-boiled eggs are my favorite style. And they MUST be eaten cold. I hate it when they're still hot. They are best on their own or on salads.
I also eat fried eggs (over hard) fairly often, on top of hashbrowns, or lately over pupusas with some taco sauce. I eat scrambled as well, though I've not been likely that as much recently. I rarely do omelettes, just too much egg and not enough other flavors.