My question is inspired by my own genealogical searching. I’ve located ancestors in England from the time of the conquest through the mid 17th century. These ancestors appear to have married exclusively with Norman families, with the women sometimes intermarrying with titled nobility. However, beyond the 13th century, I cannot find any evidence of landownership. I have discovered that some were sheriffs, but have no further vocational knowledge until their immigration to America.
I’ve frequently heard the term landed gentry, but were unlanded or landless nobles a common occurrence in British history? If so, what were their lives like?
I suspect the basic issue at hand here is just that absence of evidence isn't evidence of absence: there may be evidence that you just couldn't find of your ancestors owning land. It's difficult to say without knowing more details about your family, but it's most likely that they did have some property.
By the sixteenth century, "gentry" was being used specifically for the "lesser nobility" - baronets, knights, esquires, and all those deemed "gentle" - as a complement to the peers with a right to sit in Parliament. But the trouble is with the lower edge: who exactly was deemed "gentle"? Everyone can agree that members of a wealthy family with a large, self-sustaining estate are members of the gentry. There are various cutoff points that were used for legally defining which men could hold office or how much tax people should pay, but knowing that someone had land worth £5 doesn't tell us much about them or their social situation - except that they did own some land. (And typically there was a requirement like this for sheriffs, so ...)
There is some evidence that there was what's referred to as an "urban gentry" in late medieval and early modern England. However, it's not necessarily the case that they held no land - they often were related to larger land-holding families and did have some land themselves, they just primarily lived in towns rather than on manors. Even if the land they held wasn't as impressive as the grand magnates' estates, the fact that they owned any land at all was quite important to their social status, setting them apart from people who only owned the building that they lived in inside the town walls (or not even that).
At least in the early seventeenth century, higher offices like sheriffs were drawn from men of the upper gentry - baronets, knights, and esquires - while simple "gentlemen" did not tend to have very active roles in political/legal life on the county level. If your ancestors were filling higher offices (and marrying into titled families), they probably held some significant property - if they didn't, it would only have taken a couple of generations for them to be too insignificant to do so.
You might want to check out The Origins of the English Gentry by Peter Coss (Cambridge University Press).