if it has night flowering white flowers(which I think it is), then It is commonly known as bottle/birdhouse gourd.
In this case they will have a very smooth surface.
The scientific name is: Lagenaria Siceraria, belonging to Cucurbitacea, i.e. pumpkins tribe.
But if they had yellow day opening flowers, Then they are some kind of ornamental gourds. I cannot make a sense of the size in the pictur. If indeed they are birdhouse gourds, and they must be small variety.
As a pumpkin /squash it can be eaten when very tender and young. But it is mostly cultivated for ornamental, arts and crafts purposes. That is where the name "Birdhouse.." comes from.
If left on the vine till frost (or when the vine dies), and it is matured, it will have a hard water/rot proof shell with lots of seeds and a little pulp inside. It will take several months for it to cure and dry.

I have some of them too. But my vines just died. I started them back in May.
Cyrus

The one in the background is about 10" - 12" in diameter and 10" - 12" high already. The vine grew where a tree had fallen and I dug it out, it just appeared. I saw the first blossoms 1 month ago. It had and has White blossoms but they are there in the daytime. The gourds are mostly white with a tinge of green.
In the first message was supposed to be a link to my other post but it is wrong. Here is the correct link.
http://forums2.gardenweb.com/forums/load/namegal/msg0819245226005.html?6

Concur with cyrus, A bottle gourd (Lagenaria Siceraria) of the form commonly known as the birdhouse gourd.

Very good, Larry.
10 to 12" is pretty good size.
How many vines are there? Two gourds for all that foliage is not that many. I had about 4 vines and I have over 20 gourds.But Not all of them are 10-12". I have some from 4" to 12". My vines have expired and I have picked the gourds , because I think squirrells were having fun with them. You should leave them on the vine as long as possible, if there is no danger of rodents. Or pick them after the stems get real brown. Then you can dry them anywhere you like. Frost, freez, snow will not do any harm if they have fully matured.
Cyrus

This looks like the squash I have been looking for that we like to eat. Did you save any seeds?

fool4flowers,

What Larry has is a non-edible gourd, as evidenced by the white flowers. Squashes with this form would have yellow flowers. The squash you're probably looking for is a Cushaw type squash. Also sometimes called a Sweet Potato squash.

You can find seeds at either of the following locations:
https://www.superseeds.com/products.php?cat=128
http://rareseeds.com/cart/catalog/Winter_Squash-95-1.html

Or you could try to swap for some on the GardenWeb seed exchange.
Good Luck!
Susan

Actually Lagenaria Siceraria is quite edible. Many cultivars of bottle gourd are grown exclusively for food. They are used in the immature form.

Here is a link that might be useful: Some food type bottle gourds

I stand corrected! Thanks Farmerdilla, I never realized the hard shell gourds were edible. With this new idea, I did a little extra research and this is what I read:

Are gourds edible? Some people eat the gourd fruit when it is Very young. However as the fruit matures it has a sour, bitter taste. No, you canÂt eat them.

So I guess this explains the confusion. Most people believe them to be inedible because the mature fruits taste really bad. But young fruits might be ok to eat. But, further reading demonstrated that no curcubits native to North America are toxic. So it's just a taste thing, they aren't bad for you.

Nice to learn something new. :)

Susan

Here in Turkey some people use the "snake" form of Lagenaria as a stuffing squash. They pick them when they've gained some size but are still soft, and they have to be peeled as the skin is a bit plastic-like. Once they get too old they are spectacularly bitter though! There are some wild cucurbits in the US that are poisonous but nothing you'd want to eat anyway.