I just noticed I had a big one. Is it OK to let the plant produce such big squashes or does it hold the plant back to produce more?

Also, should they be cut or can I just break them off?

Are these squash plants everbearing and keep producing until they freeze?

Those are yellow crook neck squash. They really should be picked before they get as big as the little one you have there. The big one will be much too hard and seedy like a gourd. The little one is probably on the verge of being that way. But will probly be ok. Yes, keep them pulled off before they get that big. I snap mine off at the stem. I never cut them. Just be carefull not to break the plant.
And they will probly make good for about 3 to 4 weeks, maybe 6 depending on your weather, then start to produce only male flowers. They seldom ever live long enough to make a fall crop after living through the summer. Some will, but most plants play out and die. They are so proliffic, they just wear themselves out producing so many babies. Plus the heat and squash bugs, that will inevidebly show up, will have their way with them too.

Actually, that little one, is about the right size. That size or smaller is considered number 1 at markets. For a really good treat, if you have several plants, try picking them before they bloom. As baby squash. BIG market for that stuff at some farmers markets and niche markets.
Boil them whole or pickle.

Oh, I am glad that you showed the pictures, and the others commented, as mine are little now, and I was waiting. I didn't plant mine, I have never planted squash and the next nearest garden is probably 15 -20 miles away. I think it came in the cucumber seed, cause when it first started up, I thought it was a cuke. And I have been gardening for a long time ;-)

This year for some reason I had several volunteer plants, tomatoes, and peppers and this squash. Maybe we will have it for supper.

Thanks for the help.

The little one is as large as I'd allow them to ever get. I don't care much for crooknecks, but when I grew them I tried to pick them before they started to get warty.

The big one would be compost or chicken feed. If it was a zucchini I'd suggest grating for bread for the big one, but crooknecks seem to get much seedier, plus the seeds are tougher, than large zucchini, so I wouldn't go that route with a crookneck.

Keeping them picked will definitely urge the plant to try to produce more. Remember, the plant's goal is to produce viable seed. Once that happens, it's finished, so it pays to keep the plant trying. While it's possible via continuous picking to keep them producing until frost, most give out before then due to pests or disease.

You can eat big squash, Breezy....we cut them in half lengthwise, scrape out the seeds, and stuff them with the same mixture that we use for stuffed peppers.

But, if you let too many get big and seedy, the plant will stop producing...if one of my plants puts on more than we can eat or give away, I pickem and chuck them into the field,lol.

Oh, and you can just pull the yellow squash off, but zucchini will break off into the fruit almost every time.Better to cut them.