Hey Angel
I'm thinking that looks like a spaghetti squash. I have some growing and they have tendrils like that and are about the same shape and the leaves look simular. Of course, I have not grown any other kind of winter squash, so am not an expert.

The first one is growing up strings on a trellis with cucumbers. I'm out of trellis, so am moving in a ladder for the rest of the s. squash to climb up.

Let me take a shot at this. You said that it's a volunteer. Did you grow a couple of squash last year like a yellow and a zucchini, because I would say that it's a cross between the two. squash of the same type cross pretty easy, and It looks a lot like the cross I made once on purpose to see What it would become. The plant had the same semi vine habit and the fruit looked a lot the same though it was a lot more like a zuke not so short. the good news is it tasted pretty good and I keep the seed of the F1 cross so I could grow it every now and again and have been thinking of trying to stabilize it. I even named it. so I would say let it grow and see if you like it.

If it came up on its own and you grew more than one type of squash last year, then it's most likely a hybrid, and only time will tell if it's good to eat or not. Experimentation with crossed squash can be quite the adventure!

Do either yellow squash or zucchini have tendrils? Mine don't. So I'm thinking this is a winter squash. I've never grown winter like hubbard and such, but my spaghetti squash is definately a climber with tendrils to hold on. I'm thinking that it would not be likely that tendrils would result from crossing two plants that did not have them.

neither have tendrils that I know of but, I was told that it's likely a recessive gene in both plants and when crossed came out. they were the only two squash I had one had female (yellow) and one had male (zuke) hand pollinated and bagged. as far as the OP goes though you could be right I started my post before anyone else. it's a good guess and it looks like you my be right the fruit looks a lot like one. The plant just looks a lot like mine did like a bush with tendrils. in any event thought given the ease at which squash crosses within it's own type. then I'd say that if they grew more than one kind it's more than likely a cross of two of any given type.

Very interesting comments. Thanks everyone.

I did not successfully grow any squash last year. I remember finding some seeds on the kitchen floor one time and I might have threw them in the planter thinking that they were cantaloupe seeds.

Do you have any suggestion on when to harvest the squash? Should I treat it like a zucchini and harvest it early when it's tender or treat it like a spaghetti squash and harvest when it's very ripe?

Just found this:
http://handworkchronicles.blogspot.com/2010/12/spaghetti-and-bush-delicata-squash.html

It sure looks like what I have.

I grow Delicata squash. And that sure looks like one to me. You will know in a couple of weeks when it turns creamy white, then gets dark green stripes down the length of it. Don't harvest it till the skin resists puncturing with your fingernail, but definitely before the first real frost. Keep them in a very warm room for about 3 days, then keep them in a room that is 60 degrees or so until you are ready to eat. Cut them lengthwise to get the seeds, then cut them into moon shapes and roast in the oven with olive oil, salt & pepper on them. You will find yourself an absolute fan after you try them. I like them more than butternut. Hope you get a good crop.