This vine grows on the ground in our front yard, creeping out from under the hedgerow. We've always just mowed it. But, I am curious as to what it is. Apparently planted by previous owners. I almost ID'd it as a Hoya but not sure the stick like stem qualifies. The stem reminds me of honeysuckle without the fuzz. Seems it might make a wonderful topiary wrap.
A nearby car dealership has this as a ground cover in several areas. The lawn maintenance tech says it is jasmine. Lucky me! Maybe it will flower if we stop mowing it. Or, as my research shows, it could be a non-flowering faux jasmine, which still makes an awesome ground cover.