They're not exactly vines, but you should try raspberries and blackberries if you haven't already. They all seem to do very well here in Utah. I'm growing Canby raspberries, which are often called the 'Bear Lake raspberry' and we love the flavor.

You can grow all kinds of beans as temporary vines. And peas also in the cooler season (plant in early March, usually).

Most vines are grown for flowers rather than fruit. And there are great choices, like clematis, climbing/rambling roses, and trumpet vines (invasive, though).

I agree with the raspberry suggestion. Autumn Bliss is a great raspberry for this region. They set on 3 weeks earlier than most varieties and produce until the first frost. You can also mow them down every year since they are an ever-bearer and not have to deal with the vines or bother training them. They will last more than 10 years and produce well every year.