I know growers have selectively bred grapes through the centuries and techniques have developed in wine production but would the taste, colour and other characteristics be recognisable?
Most varieties of ancient Greek and Roman wine (the only ancient wine I know anything about) looked and smelled more or less wine-like. But they would have tasted very different from almost anything you're likely to (willingly) drink today.
The Greeks and (especially) the Romans recognized literally hundreds of varieties of wine. The Romans - history's first true wine snobs - even created hierarchies of vineyards and vintages, classified in terms of such modern-looking qualities as color (white, red, black, amber) and bouquet. These wines seem to have varied considerably in almost every respect, including alcohol content and taste. Certain characteristics of ancient production and consumption, however, ensured that all varieties tasted quite different from their modern counterparts.
Since grape must was not thoroughly strained during production, ancient wine often contained fragments of grape skins and pips, and had to be filtered through a sieve before being served. The bits that escaped the sieve must have enlivened many a Greek and Roman cup. More importantly for taste, ancient wine was stored in clay amphorae lined with pitch or resin. Most ancient wines were not aged long - thanks largely to less-than-airtight storage vessels, only a few Roman varieties lasted longer than a decade - but storage in a resin- or pitch-lined container ensured that all ancient wines tasted...well, a bit like resin or pitch.
The Greeks and Romans, moreover, almost never drank their wine neat. It was customary to mix wine with at least an equal volume of water (most of the wine tipped back at banquets was between 2/3 and 3/4 water by volume). In addition - and even more distressing to the palate of the modern oenophile - they habitually dumped all sorts of additives into their watered wine. Homer's heroes, for example, liked to sprinkle a bit of goat cheese and barley into their cups. Later, depending on the variety and desired effect, everything from marble dust (which cut acidity) to perfume (which masked the resin) was mixed into wine.
Ancient wine, in short, would still be identifiable as wine. But it was likely to be more watery, grainy, and resinous than anything on the racks or shelves today.
Just to add to the great information below, the Romans also used a wonderful artificial Sweetener called Sapa. It was made by boiling wine in a lead-lined pot to produce a kind of sweet salt that they would mix in wine.
We call it lead sugar today.