There's a short article and a long debate at the Runner's World website about the benefits (or lack thereof) of lifting for runners. It seems like this topic tends to cycle. A few years ago they used to say you had to do serious weightlifting. Then it was all about specificity and lifting wasn't as important.
I'm not sure where the debate stands now but it seems like more and more runners, both recreational and elite, are turning to core work as the lifting alternative. It may be a fad, but it's definitely popular.
I personally love core work mainly because (a) I hate lifting (b) you can do it anytime/anywhere. It's so much easier to sneak it some core exercises while I am playing with my son than it is to get a serious gym session in.
I don't have much of a core these days, but I do attempt some simple and modified yoga and pilates moves. For upper body strength I do some light lifting with dumbbells.