The tricky part of the question is not what the most important invention is, but the qualifier "in the past two thousand years". Technological innovations alter the frontier between humans and their natural habitat. Because of the insuperable importance of the environment, humans have always sought to maximize the advantage they can take from the laws provided by nature. As a consequence, truly fundamental innovations date back many thousand years ago. The most outstanding innovation of all times was probably the domestication of animals, followed by that of plants. Life in permanent homes, villages and cities, the wheel, the sailing ship, engineering, script, as well as conceptual achievements such as nations, democracy, religion, music and songs, even taxes, interest and inflation all date back way before the beginning of the common era. Several innovations suggested in this forum were actually part of every day routines of Bronze Age people, including, for instance, language, steel, paper, and reading glasses. Scientific method must have also existed in some form, since 14th century BC hydraulic installations in Greece perfectly meet the parameters of the given environment. Even moveable type was known by 1500 BC, as the example of the Discos of Phaistos from Minoan Crete shows. Finally, heliocentricity was first discovered by the astronomer Aristarchos of Samos during the 3rd century BC — but the concept failed peer reviews and its acceptance was thus delayed by 1800 years. Since the principle factors controlling people's lives today already existed 2000 years ago, the skeptic in me would intuitively vote for:nothing worth mentioning.
If we take a stroll through a Roman town 2000 years ago — and ancient Pompeii provides a good example of a city frozen in a moment of every day life — we would find a city containing factories (including one for fish sauce), public baths, athletic stadiums, theaters, plastered roads, proper sidewalks, pubs and, inevitably, brothels — facilities for people who were, for the most part, in better physical shape than us. What distinguishes a modern city from its Roman predecessor? Two things come to mind, the first belonging to the category of conceptual realization:Christianity. The Roman dominion over the western world lasted for about 1000 years — and we might indeed still live in the Roman era, if there would not have been a common denominator which united the many tribes suppressed by the imperious control. This unifying factor was Christianity. — The second prominent innovation which distinguishes a Roman from a modern city is electricity. Only through the invention of electricity is it possible to operate laundry machines and subnotebook computers; two inventions I personally cherish the most, as well as many of the other items suggested in this forum.
However, I recall enjoying a particularly Romantic evening in the usually overcrowded, noisy Cretan tourist resort of Elounda. Some time passed before I realized what made this evening so special — a general power shut down had knocked out all fluorescent lighting and loudspeakers. Lanterns and kitchen stoves still worked — with gas. This brings me back to my original response to the question, what is the most important invention of the past two thousand years. Nothing worth mentioning.