Firstly, I shall examine the passage in the original Greek:
ἔσται γὰρ μέγας ἐνώπιον τοῦ Κυρίου, καὶ οἶνον καὶ σίκερα οὐ μὴ πίῃ, καὶ Πνεύματος Ἁγίου πλησθήσεται ἔτι ἐκ κοιλίας μητρὸς αὐτοῦ.
The two words we are intereted in here are 'οἶνον' ('wine'), and 'σίκερα' ('strong drink'). The second ('σίκερα') is interested in that it is a loan word directly from the Hebrew word 'שכר' (transliterated 'shekar'). This word is rather popular in the Old Testamant (appearing 7941 times), so it is little surprise that 'σίκερα' appears 4608 times in the New Testament. The two (in both languages) are usually used in conjunction with each other, to form the phrase 'wine and strong drink' to encompass the whole variety of intoxicants. 
Wine was the ubiquitous alcoholic beverage of the ancient world. The process by which the ancient peoples made wine was simple. First, they pressed grapes into grape juice, then left the juice in large earthenware jars to ferment. Fermentation took two weeks to a month. Distillation had not yet been discovered, so Roman wine was of about the same strength as modern wine (around 13%), or possibly a bit stronger.
While 'true' Romans diluted their wine with water (roughly one part wine to two parts water), making it a beverage that could be drunk all day long, without danger of drunkenness, people living in provinces, such as Judea, are not supposed to have done so. That said, it is likely that the Roman officials did dilute their wine, in keeping with the custom back in Rome. Because of this, it is also likely that citizens wishing to curry their favour might also have adopted this custom. The Greeks also diluted their wine (roughly one part wine to four parts water). 
Other alcohols included beer, which became significantly less popular than wine. In particular, wealthy Romans looked down on the drinking of beer. Tacitus (writing much later, in the 1st Century AD) wrote disparagingly of German beer. Barley wine (a type of strong ale, roughly 6-11%) existed, as well as alcohols made from whatever fruits might be growing in the vicinity. For example, when Caesar arrived in Britain in 55BC, he found the locals drinking an apple cider, a custom he and his men adopted with enthusiasm. 
I have not be able to find any evidence for the consumption of distilled spirits or liqueurs.
Abstaining from alcohol was not as easy then as it might be now. Since a large proportion of running water was (and still is) undrinkable, ancient peoples turned to alcohol (in particular wine) as a daily staple, giving them the fluid they needed. The water mixed with wine would be (somewhat) sterilised, allowing it to be drunk, and making the wine go further. One assumes that John must have drunk water only, or at least non-alcoholic juices (grape, etc.). There is reference in the bible to non-alcoholic wines, although this is rare.