There are three types of wine drinkers: those who only drink dry wine, those who only drink sweet wine, and those who drink both depending on the circumstance. I am in the third camp, and I think the first two camps are misguided.
The first camp, those who only drink dry wine, usually do so for a couple of reasons. One, there is a common misconception that sweet wine is inferior wine, not suitable for serious wine drinkers. Two, there is so much bad sweet wine on the market, these people have tasted a few that were horrible and concluded that sweet wine is bad. What I would say is that good sweet wine, such as some German Rieslings or Alsace Gewurztraminers, would not have the same flavor profile if they were not sweet. In other words, it's not just a regular wine made sweet, the sweetness is integral to the wine, and if you removed it you would lose a lot more than just the sugar. As for reason number 2, here's a good way to tell if wine is good sweet (and naturally sweet): check the alcohol content. It should be lower than dryer wines, for the most part. Remember that it's the sugar in the grapes that has been converted to alcohol, so more sugar should mean less alcohol. Otherwise the wine has probably been sweetened with sugar or grape extract, and will likely taste bad.
Occasionally, but rarely, I have people tell me that they don't like sweet. I just plumb don't believe that. Unless you don't like the taste of sugar, don't drink sodas, and don't drink cocktails, there is no reason to say that it's the sweetness in the wine that turns you off. Also, remember this: the sweetness you taste in the wine (assuming it's natural), comes from the grape. And the grape, in its unpressed form, is even sweeter than the wine! How often would you complain about a fruit being too sweet?
To those who only drink sweet wine, I would say this: try having wine with food. Dryer wines tend to be more food-friendly, and it's only by pairing wine with food that you can develop a true appreciation for it. If you only drink wine by itself you're missing out.
So, to the sweet wine skeptics: try a single vineyard German Riesling Spatlese, keep an open mind, and you may be surprised.