Stoli: a spirit that hearkens back to a time when Vodka was exotic and sophisticated. A far cry from the present day, where as Ron Swanson so eloquently stated, "clear spirits are for rich women on diets."
So let's get this out of the way first: trying Stoli—which might be the name-brandiest of vodka name brands—I was expecting it to be bad, and it really wasn't. But I would argue that we're quite a long way from being great. If anything, Stoli is a shining example of a neutral vodka that doesn't have any angles, edges, or quirks. For better or for worse, when you think "Vodka," you may as well think "Stoli."
For me, personally, vodka isn't synonymous with neutrality. St. George's "All Purpose" vodka is delicious and characterful, as is Russian Standard Gold, and I quite like Belvedere. If you're willing to sit down and appreciate a vodka on its own terms and delve into subtlety, there are indeed vodkas worth paying attention to. I'll go to the mats on this one: there are aromas and flavors in vodkas as a general category. If you know where to look.
Stoli, however, is an altogether different proposition. Its mission is to charge up the hill of inoffensiveness and defend it at all costs. From what I've read, Stoli goes so far in its production process that the spirit is filtered through sand, cloth, and charcoal. No pesky tastes getting through that blockade! Now, when Stoli entered the US market so many years ago, I can understand (in an academic sense) how it was a shot across the bow of strongly-flavored brown liquors, and even strongly-flavored white liquors like gin. That was its story, and its sticking to it.
Stoli doesn't smell like anything, and it doesn't taste like much. I sussed out a little bit of lemon and kumquat soapiness when I really took the time to analyze it in a straight tasting, and generally the mouthfeel is lighter and lither than most brands. I should mention that Stoli is fairly generous in the finish, where there's some rye influence in the form of peppery spice and a little bit of sourdough bread. Still, that's not a ringing endorsement for enjoying it straight.
As a mixer, I would imagine this would work pretty well if the best vodka for your application is one that gets out of its own way. For me though, I like things that taste like things, and generally I don't make cocktails like Screwdrivers or Greyhounds where the end result is alcoholic juice that doesn't taste as much like booze as you'd expect.
For that reason, I'll admit my own bias here. Stolichnaya is a sterling example of a neutral spirit, but it's got little reason to hang around on my shelf. It's a great vodka for people who probably have no interest in this site or anything I have to say.