According to a raft of new research (and this great article in the WSJ), the answer is yes, profoundly. We've all heard about how Eskimos have forty or more words for "snow" (something of an urban legend, by the way), but there are even more amazing (and actually true) examples of cultural differences borne out through language. For instance, did you know that Russian speakers, who have more words for light and dark blues, are better able to differentiate between different shades of blue? Stranger still, the Australian Aboriginal people of Pormpuraaw don't use words like "left" or "right" -- they refer to objects in space only by their absolute ordinal directions, ie North, West, East, South, South-east and so on.
In Pormpuraaw you say things like, "There's an ant on your southwest leg." To say hello in Pormpuraaw, one asks, "Where are you going?", and an appropriate response might be, "A long way to the south-southwest. How about you?" If you don't know which way is which, you literally can't get past hello.
As a result, the Pormpuraaw people are exceptionally good at orienting themselves in space. As are the speakers of many other languages around the world that rely on absolute directions in everyday speech. The thesis here is that knowing itself is also influenced by language. Some very basic methods of interacting with the world around us change depending on what language you speak. (Also, it's been proven that bi-lingual people think differently as they switch between languages.)
More surprising examples:
• The Piraha, whose language eschews number words in favor of terms like few and many, are not able to keep track of exact quantities. • In one study, Spanish and Japanese speakers couldn't remember the agents of accidental events as adeptly as English speakers could. Why? In Spanish and Japanese, the agent of causality is dropped: "The vase broke itself," rather than "John broke the vase."
In other words, writes Lera Boroditsky, the author of the WSJ article and a psychology professor at Stanford, "All this new research shows us that the languages we speak not only reflect or express our thoughts, but also shape the very thoughts we wish to express. The structures that exist in our languages profoundly shape how we construct reality."