All cultures would have a basic fermented beverage made of yeast pitched in a sugary broth made of agricultural products.

Wines, ciders, and other beverages of fermented fruit juice are probably your lowest-tech stuff.

Mead is fermented diluted honey; that's also very low-tech and low-infrastructure, so it falls into the category above. 

If you have livestock or riding animals that produce milk with fermentable sugars, you can also put yeast in that and get alcohol. 

Someone above said something about fermented cerebrospinal fluid. If it doesn't kill yeast and it's got sugar in it, it'll work, so go nuts, illithids. (Also makes me think, if elder pool 'juice' can support yeast, either raw or with a little processing, you've got some awesome flavor for that next bottle of Drow wine you loot off an Underdark caravan.)

Grains go into beer, but only after you've malted the grains - gotten them to start the germination process, so that enzymes within the grain start turning starch into sugar. So you really need at least basic agricultural skills and enough infrastructure to take a bunch of grain and malt it, and you're likely to start to have a bit of experimentation going on as cultures realize that if they heat up a mash tun full of crushed malted grain *just a bit*, it works better (due to better enzymatic activity), but if they do it too much, it stops turning sweet. For that reason I really don't see any stereotypical hunter-gatherer D&D races or cultures making it to beer. Barbaric northern raiders who don't grow grain are not going to have beer, stout, ale, anything like that, they'll be drinking ciders and meads.

Beers and ales also tend to need a preservative additive; they do have *some* alcohol, but they're low enough alcohol that they can spoil or get mold in them. Nowadays everyone uses hops for beer; before that, we'd use other herbs (that was called 'gruit', it's interesting research). 

Hard liquor requires a still and enough of an understanding of distillation that you can use it and isolate ethanol from its less fun friends like methanol and other fusel alcohols. So, you want a culture that has alchemists, and is capable of building a still with its blacksmiths. At that point, you take whatever it is your culture made before it got that advanced, and turn it into vodka in the still.

You have a few different classes of spirits, which I'm going to generalize wildly and call "vodka", "gin", and "whiskey". Vodka's right out of the still. If you have any extra "taste" to the tastelessness of ethanol, it's trace amounts of stuff that managed to make it through the distillation process. 

Gin, as I'm describing it, takes vodka that's been distilled and adds "botanicals" - any sort of herb that has alcohol-soluble flavor components. So if your race has alchemists and a spice that's real important in that culture, they're pretty much guaranteed to make a gin out of it. (We pretty much only consider gin to be gin with juniper berries, but here I'm just using 'gin' to mean 'ethanol you soaked some stuff in to get the good stuff in solution with the ethanol')

Whiskey, as I'm describing it, takes vodka and ages it either in or with something that takes a while to leach into the final drink. The standard example in the real world is charred oak barrels. You take ethanol made from corn mash if you're in Kentucky, or barley mash if you're in the Highlands, and you put it in a barrel of oak for a few years, and you get a nice brown liquor.

All that stuff at least requires a still, the basic beverage you want to distill, and the ability to age the resulting liquor. You're likely only going to find it in reasonably advanced societies. A nomadic, hunter-gatherer tribe is not going to have a good way of making any of it.

You can also jack, or freeze distill, stuff. That just takes a wine or cider and a cold climate. So that's a way for primitive cultures to get something up to about 40 proof (20% ABV). You take the barrel of whatever you want to jack, and you put it outside in the winter. Water freezes out of solution, and you skim out the ice cubes and throw them away. The alcohol stays in and gets concentrated. So, your northern cultures, they'll definitely have this; it's one of the most obvious alcohol making accidents to happen, and it works, so they'll use it.

Fortified wines are interesting and I think in a multicultural D&D society, they'd spring up in interesting places. You make them by taking a normal wine, and then adding a distilled spirit to it (to "fortify") it. You can also add some way to make it sweeter. You do this to further preserve the alcoholic beverage (if for some reason the 12% abv is going to spoil somehow) and also to stop yeast activity, so it doesn't keep fermenting until all the sugar is gone (leaving you with a very dry wine or whatever).