Looks like a Clematis seedling. You won't be able to tell what sort of Clematis until it flowers.

Clematis was the first thing that came to mind for me too....

I thought clematis as well, but then I noticed it wrapped an "arm" tightly around a wire cage I placed over it. Very tightly, and I thought clematis don't wrap?

Absolutely clematis. They climb by wrapping their leaf petioles round anything they encounter.

Well I'll be very happy with another clematis! Hope it doesn't mind lack of climbing support for now. I'll have to try string from the wire cage to some wires a few feet above. Otherwise I really hope it will get bushy at the top of the three foot cage it has now. The most unfortunate thing is the location which will soon be in 80% shade (two to three hours of early morning sun through a chain link fence, then dappled shade for a few hours and then full shade from about 2pm on.

Thank you for your help!

That's why I don't like to pull mystery plants until I know what kind of plant they are or blooms they produce. It seems to have come back this year so the limited sun that it is getting seems to be enough to keep it going (whether you get lush blooms, we'll have to wait and see)

I wanted to update this post so here I am. I had no experience with clematis when I posted the original message on here. Had never heard of them even if I probably saw some here and there and only found out what they were after I saw the neighbor's growing on our fence and looked it up. Last year (2014) this clematis grew to maybe 4 or 5 feet and just stopped. The leaves were pretty small to begin with and they stayed that way, and no buds ever appeared so I did not find out what it was. But I kept it watered and hoped it would grow back this year. It did! And from the first signs this spring, it was coming back much stronger! The leaves are more than double the size they were last year and it just shot up. I bought a real trellis for it too as I hoped to see blooms this time and it seems to be a good fit. The trellis is 6ft and about 10 inches are below ground. Just from looking, I think the clematis grew about 9 feet total, and the growing tip has ended in a large bud, with buds growing out from the base on either side so I'm pretty sure it's done growing in length. There are about 15 buds total. Even though the top is in shade all the time, the bottom still gets a little morning sun so I think the flowers should be nice. Can't wait to find out what gift a previous tenant left behind!

And here are the blooms! Most 4 petals but at least one has 5 petals. Largest flower maybe 4 or 5 inches across.

Thanks for the update! It looks quite happy where it is.

This winter while the vine is dormant, perhaps in February or early March, cut off the vines leaving a couple of sets of buds. This is called hard pruning, and will make the vine bushier next year with more vines growing from the base of the plant. It will also have more blooms lower on the plant as well as on top since this appears to be the type of clematis that blooms on new growth. If you don't prune it, it will be more full at the top and bloom at the top, but won't get a whole lot more full at the bottom or bloom as much lower down. You may eventually find that it outgrows this size trellis.

Thanks! I left it out of my update, but I did cut it down this year to about 8 inches tall, just as I did with my purchased clematis. But none of them produced more than 1 stem still (before dying off in the case of the other two). Maybe next year?