Depends on the alcohol. It took me years to figure out what I enjoy and what I despise. Everyone I know has this one drink that they abused and can no longer go near. For me, it's tequila. After having an incredibly rough hangover from a long night's session of tequila shots, it took me about ten years before I could go near a straight shot of it again.
For cocktails, margueritas and daiquiris were what got me into alcohol. I still really enjoy them, now that I can stand the smell of tequila again.
In general, for hard liquor, we have a very nice collection of Scottish single malt whisky. My favourite is Caol Isla, which is a very floral, smooth whisky from Islay. My husband and I immensely enjoy drinking whisky neat - no water or ice to cut it. I can spend about half an hour sipping a single shot of Balvenie Double Wood. The point is, I enjoy the taste - it's not about getting drunk.
That being said, I don't enjoy Irish, American or Canadian whiskey/whisky. If I'm drinking one of those, I'll usually mix it with a soft drink - usually coca cola. I do not drink blended whisky of any type - life is too damned short to drink blended whisky.
As for beer, all American beer I've ever had is pretty much terrible. I never enjoyed it in America, and when I moved to the UK, my British friends took great delight in introducing me to what they referred to as "proper" beer.
Now, if I'm drinking beer, I stick to Czech, Belgian and German pilsners. Budweiser Budvar is one of my favourites - it's the original "Budweiser" and about a million times better than the American version. Staropramen and Weihenstephan are the other two I'll drink happily. But again, it's about the taste, not about getting drunk (though a few pints of any of these beers will get me reeling in no time). In the summer, I love having a pint of Hoegaarden with a slice of lemon.
Oh! And I have a very HUGE soft spot for Dos Equis, but I should add that it is actually a German pilsner-style beer, which is why it's so good. The fact it's from Mexico is just incidental.
Otherwise, I'm very partial to real ales - particularly from tiny ale houses that dot up and down the UK.