Beers:

• Beers are likely as old as grain agriculture itself. Early beers were a mix of grains, grapes and honey as well as various herbs. Unless someone was sampling during fermentation it would be flat (un carbonated)
• The ancient Mesopotamia beer would be served with the grains still floating in them. People would gather around big basins and drink through long straws. It likely wouldn't taste great to our modern tastes. It would be bitter, somewhat thick, probably had some funky flavors and no carbonation.
• Beer starts to take a slightly modern turn in northern Europe in the early middle ages. Along with the barley they would add a mixture of herbs called gruit. We don't know what was actually in gruit but it probably had some rosemary and other herbs like bog myrtle. Besides ar herb-like flavor it would also add alot of bitterness. At this point barrels are being used to store beer but except in fringe cases most people's beer would still be flat. Reusing barrels would add an environment for various types of organisms like brettanomyces yeast and lactic bacterial to occasionally flourish. While these can be considered spoilage organisms that can also create tangy, spicy or funky flavors and aromas. You might also have some wild yeast that create a balsamic or nail polish remover aroma in some batches. Once those organisms where in a tank or barrel they would contribute to a consistent style. Perhaps even for a whole brewery.
• In the late middle ages they begin using hops instead of gruit. These hops were "noble hops" and did not have the fruity/pine-like flavors of the native American hops that you might find in an American IPA these days. Mostly they would just add bitterness like gruit did. Again, most beer would be flat or perhaps lightly carbonated in cool areas but its beginning to taste like modern ales.
• The next big evolution towards styles that are currently popular styles would be the development of lager (clear and mostly light beers) in the early modern period. These beers would be brewed slowly by special yeast in cold subterranean cellars in Germany. This style would really start to flourish in Germany during the 19th century and would eventually become the dominant international style. It was also during this era that corks and glass bottles would start being used which would help preserve carbonation more consistently.

Wine:

• Wines also began being fermented around the time of early agriculture. These early wines would taste more tart and thin than what we are used to now and would also be flavoured with bitter tree sap and herbs. They would also be heavily oxidized with a sherry-like character and tart with flavors and aromas of vinegar.
• This basic style would continue up to the greek/roman eras. In early roman eras wine would range from a very light vinegar flavoured beverage consumed by the poor and soldiers to thick syrupy "dessert" style wines made from nearly dried grapes. Wines would usually be diluted with water (sometimes even salt water) and often flavoured with aromatic herbs, burnt pine tar, honey, boiled juice concentrate and even lead (for sweetness).
• Eventually the tastes for robust Mediterranean style wines would be replaced in the empire by the more elegant and nuanced wines that came from Gaul.
• From late antiquity until the early modern period wine style was fairly static. The celts developed the first barrels and wines produced in Gaul from this period forward would be exclusively stored in wooden oak barrels. The oak would add sweet vanilla like flavors and also flavours of wood and char. If you lived near a wine growing region you would get to drink fresh wines with sweet floral/fruity aromas and flavors. If you lived farther away from a wine region there would be a greater chance that the wine you tried would be vinegary and oxidized. Especially if you were served from partially full barrels.
• Just like in modern times the tastes of the export markets in the middle ages dictated the style of wine produced. The english during this period had a preference for rose-styled wines from Bordeaux and racy white wines from Germany. They also enjoyed the dried-grape dessert wines from the Mediterranean wine growing regions. Other areas like the low countries had a preference for richer and more robust wines.
• Wines during this period might be drank undiluted or diluted. They might also be flavoured with herbs, spices and honey. A popular spiced wine mixture was called Hippocras and had ginger, cinnamon, pepper, honey and other spices mixed with red wine.
• During the middles ages the very poor might drink thin wines made re-watering pressed fermented wine grapes
• Towards the end of the early modern period in the 18th century Europe began a major transformation in the development of large urban cities. The poor that flocked to these areas didnt want "fine" wine, they instead wanted wine that was as cheap as possible so it was grown in cool northern areas on heavily over-cropped vines that produced thin simple wines of not much character.
• In the 19th century sulphur, bottles and corks came into use so the wealthy started aging their wines. For the first time people were introduced to a new style of wine that was aged into new and complex flavors yet not oxidized.
• There were styles of oxidized wines that were popular that were grown in southern hot climates and fortified with spirits like brandy. Examples would be Port, Sherry and Madera.

Maybe you can tell by following this, one of the oldest recipes in the world:

It is you who handle the.. dough with a big shovel, mixing, in a pit, the beerbread with sweet aromatics. It is you who bake the beerbread in the big oven, and put in order the piles of hulled grain. It is you who water the earth-covered malt; the noble dogs guard it even from the potentates It is you who soak the malt in a jar; the waves rise, the waves fall. It is you who spread the cooked mash on large reed mats; coolness overcomes It is you who hold with both hands the great sweetwort, brewing it with honey and wine. You place the fermenting vat, which makes a pleasant sound, appropriately on top of a large collector vat. It is you who pour out the filtered beer of the collector vat; it is like the onrush of the Tigris and the Euphrates

• Sumerian Hymn to Ninkasi (ETCSL Translation: t4.32.1)

hi! there's always room for more input, but meanwhile, check out these previous related threads

Sunday AMA: The History of Wine, Beer, Cider and Mead

How do the wines of history stack up against what you can readily buy today?

What did wine and beer taste like in ancient times? Did it resemble the beverages we know today?

What is the difference between modern day wine and its ancient (BC and first couple hundred years of AD) counterpart?

As you might find in those other threads, beer as we know it primarily gets its flavor from hops. Hops are a flower used to add bitterness to balance malted barley's sweetness. They also act as a preservative - here's a nice summary and here's an older and much more in depth article about that for those who care. I couldn't find anything else that wasn't behind a paywall, but the acids and compounds (humulone and lupulone) in hops act to slow/prevent bacteria from consuming the sugars in wort (unfermented beer) before the yeast does.

Now, as far as we know, hops first became widely used in beer in the 11th Century in Germany. Prior to that, most beers would have been brewed with a mixture of other native herbs called "gruit." That mixture was basically whatever people had handy or whatever they wanted to put in their beer. That style has seen a bit of a small revival lately, and beeradvocates has a page on the style here.

So to answer your question: no. Prior to the 11th Century, most beer produced around the world would have tasted quite different from those produced today. And remember, beer and fermented beverages have been produced since the dawn of civilization, so the use of hops in beer, seen as standard now, is actually quite a recent invention.

And, sorry I can't really speak about wine, but I'd venture a guess and say that it has remained more or less similar to early wines, because there are fewer components. The only ingredient needed to make wine is grapes, or another fruit/berry. But I'll let someone more knowledgeable answer that.

Dogfish Head has a series of beers entitled "Ancient Ales". They're basically beers which they've collaborated with some experts on early beer recipes. They're website has some good information about the specific beers that they've created. I do not know whether any of these are currently on the shelf.

http://www.dogfish.com/ancientales