That looks like a weed that has plagued my garden for a decade now. It's a curcurbita (member of the squash family). If you allow it to grow, it will eventually cover other plants. In my yard it covered 2/3 of a small tree before I got an ID and started ripping it out of the garden. I've still not managed to get rid of it entirely, so beware.
I'm not sure whether any wildlife will eat the fruit/seeds. My guess is 'no', since my plant was covered in fruit even when I had a yard full of birds by day plus raccoon guests by evening.
Ok. Looks like I was wrong about the curcurbita thing. (It was cucumber, not squash.) Here is the thread where I asked for ID's for the one in my garden. Apparently, the only picture I had showing the weed was the lily pic with the weed in the background on the left. Link: http://davesgarden.com/community/forums/t/486711/
I noticed that in both cases if you read the comments in PF, people describe them as 'positive' and indicate that the fruit is edible (for humans). According to the comments, M. pendula tastes like cucumber, while M. scabra tastes like a pickle (sweet/sour). If you are willing to taste one of the fruit (very small taste), you may be able to determine which it is that way.