There are countless vineyards in Greece. The Greeks love their wine and drink plenty of it. All together red wine is more popular than white. There are exceptions obviously but as a general rule it works. Local wine is quite cheap when you order it in a taverna but even bottled wine is a lot cheaper especially if you compare it with prices in the UK and Ireland.
 
Put it this way, the local wine they offer in tavernas wouldn't win a medal and to a French most likely is disgusting, I personally like it a lot especially in certain areas like southern Crete. It is rather sweet, quite strong and with 2-3 Euros for half a litre dirt cheap. It comes in an open carafe. Ask for grassi with a sharp s and you order a kilo rather than a litre. I never found out why they measure in kilo rather than in litre but I am sure there is a perfectly good reason. The idea of a pint never appealed to me either until I found that with two pints you actually get more than a litre. I like that.
 
In very touristy areas like Santorin or Mykonos it might be difficult to get open wine. If a waiter tells you they don't have open wine you basically know you are sitting in a tourist trap.
 
In most places they do have open wine and it is perfectly fine to ask, if you can try it first. In most small tavernas they serve their own wine and the owner will gladly drink a glass with you. If you don't like the wine be polite and order it anyways. From my experience after a few glasses it doesn't really make a difference anymore.
 
Quite common is Retsina. It is white wine with resin and well put it this way. There are people who like it but most people find it repulsive. When I first tried it  I went to brush my teeth. Some Greek friends later explained me that there are huge differences. The cheapest Retsina is generally the best and it does take a while to get used to it. Drink a bottle and you will know if you like it.
 

Beer

 
A popular question is: What is a typical Greek beer? Back in the old days the answer would have been Heineken and Amstel. At this stage there are local beers as well but most of them are disgusting. Mythos is OK but allegedly gives you a bad hangover. Well at least it is cheap. A bottle in a bar will cost between 2 and 2.50. Again, if you are in a touristy area they will charge you 3-4 Euros.
 
Only recently the Greeks discovered the beauty of draught beer. It is a lot more common these days.

 
Ouzo

Ouzo is probably the most famous Greek liqueur. It has a very distinct taste. It is basically brandy with an Anis taste. It's quite cheap and strong. You get it everywhere, sometimes even for free after a meal. Here is a little trick. I find the taste let's say below average. However, if you mix it with water (about 50:50) it suddenly tastes quite nice and refreshing. Get some ice as well and you have a not only nice and but really cheap long drink.

 
Raki (Tsikoudia)

In most parts of Greece people would drink Ouzo, Crete is different. They don't consider themselves Greek anyways. They are Cretans first and to them Athens is as far away as Brussels. What they have in common: They want from the Cretans and give nothing in return. And this is how popular they are.
 
Of course the Cretans have their own national poison and it is called Raki. Raki has up to 70% alcohol and you never know how strong it is. The really nice tasting Raki is the strong one by the way. Raki with 40% is just wrong. It is distilled in old local distilleries and there is a good reason. The old places don't have to pay tax. You would build one now the government would charge you so they just keep the old ones or do it illegally in their backyard. Raki is dirt cheap. If you drink to get drunk that's the one to go for. Don't forget to drink plenty of water. The stuff is vicious.
 
 
Non alcoholic beverages
 
Besides the standard lemonades like Fanta and Coke you have a few local brands. As an alternative to beer I'd personally choose fruit juices. They are really nice in Greece and that shouldn't surprise you. The more sun an orange get the sweeter it gets. There is plenty of sun in Greece.

Water

In most places you can drink tab water on some islands you shouldn't. I can't give a general advice other than: ask the locals if the water is fine. Bottled water is relatively cheap. It has to be, after all it is a hot country and generous supply with drinking water is essential. Always make sure you drink plenty.
 

Coffee and tea
 

Greek coffee is served in tiny cups and quite strong. It's not bad but quite frankly most people don't particularly like it. For example it is not filtered. The loose coffee ground is in the cup. Most people these days are not used to drink their coffee "Turkish" and find it disturbing.
 
The taste itself is fine. Greek coffee is served very sweet (gliko), just sweet (medrio) or without sugar (sketo). Very common is Nescafe. You can get it as a hot cup of coffee or cold as Frappe. I initially dismissed the thought to drink cold coffee but Frappe turned out to be really nice. Especially on a hot day it is my first choice.
 
In some places you also get filter coffee. It is called "galiko kafe". Literally translated that means French coffee.
 
A good alternative is tea. Don't expect too much though. You won't get English breakfast tea. Herbal teas from Crete for example are quite nice. To play it safe I would just bring my own. I'm sure you are well aware it is almost impossible to get decent tea on the continent.

 
Pubs and bars
 
 

The "Kafenion"

The coffee house is a traditional place. It used to be the meeting place for the men, women were not allowed. It is a bit more chilled out these days and only in remote villages you will find the men sitting there while the women gather next to it. You are welcome to join in. Most of the old men will probably speak some English and they are generally very friendly.
 
In these coffee houses they serve coffee, Raki (on Crete), wine and cold finger food. Sometimes you even get it for free. In some Kafenions you will also find a menu. That's rather unusual though.

 
Bars and Disco