I don't know if it can really be referred as a state in the modern sense, but a good example would be the Roman Empire. Rome annexed Greece and the Near East in the 1st and 2nd centuries B.C., in which territories the Empire survived after Rome itself fell to the Germanic invaders in the 5th century A.D.

There are many examples of this in pre-modern eras (think of the Norman kingdom's gradual evolution into England, for instance) but for a wide variety of reasons I think it would make sense to discount anything before the advent of the Westphalian state system and the birth of nationalism. A lot of medieval kingdoms held shifting domains, but that didn't necessarily effect some peasant farming some local lord's land somewhere.

A dramatic modern example is Poland. The modern polish state has slid dramatically westward during the twentieth century.

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