Is there any difference between cheap and expensive vodka?
Here's a report on an informally conducted taste test suggesting that there are indeed detectable differences between various vodkas: (the report does not say so, but I suspect that much like wine, whether one vodka comes out as better as another one has little to do with its price, except at the very bottom end of the price range)

And, yes, there are differences—a truth known by anyone in the liquor industry with a little sense. But one that is frequently forgotten— partly because our government insists on characterizing vodka as a &quot;colorless, flavorless, odorless&quot; beverage; [...] That there are subtle, and sometimes dramatic, differences in flavor and odor between one vodka and another was driven home recently by a daylong seminar hosted by Absolut. [...] Central to the event was a blind tasting of 12 different vodkas. [...]
The main lesson of the tasting—or re-learned lesson, since many of us in the room knew it already—is that the biggest difference between the flavors of various vodkas derives from the source material, and that difference is easily detected, if you pay attention. Vodka can be distilled from anything, but the most common raw materials are grain and potatoes, with a few using molasses and grapes and other things. Grape-sourced vodka typically has a fruitier character; grain-sourced has the expected bready, yeasty and, yes, grainy notes, with the rye vodkas having more bit and spark than the barley or wheat ones; and potato-sourced vodka has a rounder, sometimes buttery flavor.
From: http://offthepresses.blogspot.be/2010/03/vodkas-and-their-differences.html

Another taste test conducted by the New York Times suggests the same thing:

Delving into the world of vodka reveals a spirit unlike almost any other, with standards that make judging it substantially different from evaluating wine, beer, whiskey or even root beer. A malt whiskey should be distinctive, singular. The same goes for a Burgundy or a Belgian ale. But vodka? Vodka is measured by its purity, by an almost Platonic neutrality that makes tasting it more akin to tasting bottled waters, or snowflakes. [...]
A lack of distinctiveness is a separate matter from a lack of distinction. The vodkas we tasted had character and their own flavors and aromas, even though the differences among them were often subtle and difficult to articulate. [...]
That being said, at the end of our tasting it was Smirnoff at the top of our list, ahead of many other names that are no doubt of higher status in stylish bars and lounges. [...] The prices of these vodkas ranged from a low of $13 for the Smirnoff to a high of $34 for Potocki, a Polish vodka that did not make our cut. The Belvedere also cost $34, but that was for a liter rather than the usual 750 milliliter bottle. Imported vodkas tend to cost more, partly because of taxes levied by various governments, currency exchange rates and, not least, marketing concerns: as has been proved in many industries, wine not least of all, raising the price of a product increases its status among consumers.
From: http://www.nytimes.com/2005/01/26/dining/26wine.html

As a counterpoint, here's another report suggesting most people can not tell the difference:

To summarize our findings,

Given a particular brand of vodka, people prefer its taste after it has been filtered, but this is most likely because filtration reduces the alcohol content.
Most people can’t tell the difference between an expensive vodka with high alcohol content and a cheaper vodka with lower alcohol content.

Our second experiment demonstrated approximately equal preferences for Pavlova and Ketel One. Although Pavlova contains 3-5% less alcohol by volume than Ketel One, it is also 70% cheaper, so it would seem a clear winner.
From: http://www.monzy.com/vodka-research/