Get ready, this is going to be tl;dr.
In a nutshell, I think it's unclear and complicated. The intersection between psychology and linguistics is particularly murky when you're talking about this, but there are many interesting people writing about it.
Here's a recent NYT article by Guy Deutscher on this subject:www.nytimes.com
In the article, Deutscher lays out the evidence in favor of a weak version of the Sapir-Whorf hypothesis:en.wikipedia.org
He essentially argues that although language may channel/shape thought and even influence our perception of the world (see the bit on geographical orientation and colors), it does not prevent or "forbid" us from thinking certain thoughts. I think the bit on colors is especially cool - look up the studies by Berlin and Kay for more info on that.
Overall, I think his analysis is a very reasonable treatment of a subject that many linguists wouldn't touch with a ten-foot pole.
The reason for the ten-foot pole is, basically, Noam Chomsky. His conviction that the building blocks of language and thought - the capacity for performing every language - are innate, universal and little affected (I exaggerate, but so does Chomsky) by society and culture has been taken as canon for many years.
Recently, a guy called Daniel Everett challenged Chomskian doctrine with his studies on Pirahã, a language from the Amazon, that has some very peculiar traits:en.wikipedia.org
After living with the Pirahã for several years, Everett concluded that the lack of certain elements in the language had profound effects on thought: The Pirahã couldn't learn to count, they didn't draw or paint, they had no creation myths or communal history past a few generations back, and they didn't seem to have a sense of time in any Western sense. Most startling of all, they didn't have recursion: en.wikipedia.org
Chomskian theory holds that ALL human languages have recursion: Indeed, that's the argument Chomsky, Hauser and Fitch use in a 2002 paper to refute (sort of) the idea that animal communication systems can be called "language", because we haven't found evidence that, say, dolphins can deal with recursive structures... That may be because we haven't tried that yet. We're working on it.
Cultural relativists reacted with horror: Common PC thought on this is that no culture, language, or group of people is inherently more "primitive" than any other. The thought that one's means of communicating ideas could stunt one's capacity for having ideas was not a comfortable one.
Chomsky hasn't commented much on this, but there's a definite air of dismissive condescension wafting down from his ivory tower.
Speaking as a relatively informed amateur, I have mixed feelings about this. I don't think it's quite defensible to take anything but a very nuanced, qualified position on the whole argument, and I think Deutscher does a good job of explaining the evidence while keeping his ass planted firmly on the fence.