Looks like mulberry to me, with lots of unripe berries.

Mulberries are delicious. Birds and wildlife think so too. Unfortunately, that's how it's seeds end up everywhere. I have a neighbor with a mulberry tree in his yard and get them popping up all over the place.

Hi CaraRose, thanks so much for the response. I did some Googling for the best way to remove a mulberry tree...but it doesn't seem like there is such a consensus. Any tips for how to best go about it? Thanks again.

Once they're established, I'm not sure. We have one in the fenceline of my garden, and I've been cutting it down every year and every year it tries to regrow. When they're seedlings, I pull them.

I think if the one in the garden was in a different spot, I might try painting the leaves with roundup. But the damn thing is right next to my cukes and tomatoes, so I'm afraid to use weed killer there.

One of the regular posters in the Trees forum says the best way to get rid of woody plants is:

cut the plant down. Get undiluted Round-up (or generic equilvalent) and put (squeeze bottle, paint brush, or the like), across the surface of the stump, making absolutely sure to get it along the inside of the bark line (as that is where the growth takes place - remember xylem and phloem from high school biology?). He recommends putting a bit of oil in the Round-up to slow down the drying, so it can really sink into the plant.

You may have to repeat this, as some trees just never give up, but if you keep it from sprouting new leaves you should be ok. Good luck!