IME, zucchini doesn't climb, but supposedly you can tie the vines to a support as it grows.

Is climbing zucchini available? Seems like the cultivars are usually bushy.

Zucchini, unless a "bush" variety, zucchini grows as a stout vine. It is not a climbing vine, however, and must be physically tied to a supportive trellis.

'Tromboncino' is in the same species as butternut squash but can be used as a zucchini substitute while young. It is a vining plant. Huge vines, actually. As for actual zucchini, I have only seen bush varieties.

Rodney

I have always grown zucchini as a bush, except for a variety called "trailing zucchini". I have seen many pictures online that show particularly the "yellow" squashes grown on a trellis, but I have never tried that. Butternut and other winter squashes, in my opinion, are too heavy for trellis and may stress the stems to the breaking point.

I have never had an issue growing winter squash vertically. The stems do not break and the fruit doesn't rip the vines off the trellis. You just need to make sure the trellis itself is sturdy and can support the weight of the vines and fruit. I don't have a pic of it growing but the warted pumpkin on the left, which was 10-15 pounds, was grown on a chain link fence a few years back. Vines were fine, fruit were fine, and no sling or netting was needed under the fruit.

Rodney

As already mentioned, zucchini come either as a bush or the original vining variety. And, they can be tied-up on a trellis. I don't think they do as well, but that's just my experience. The weight of the zucchinis won't be too much; for winter squash that is trellised I would make a sling tied to the trellis for each squash to help carry the heavier weight.

I Ihave found that the bush zucchini will vine IF they stay healthy long enough.

You might take a look at Armenian Cucumber. It's called a cucumber but I use it as a zucchini. It can be eaten raw or cooked like a zucchini; it's quite tasty! I have always grown mine on a trellis and it does fine.