Language in Ukraine
Ukraine is quite an interesting country in regards to language. Currently, Ukrainian is the only official language recognized across the entire nation. In practice, however, Ukraine is very much a bilingual country with a roughly 50-50 split between Russian and Ukrainian. According to an official 2001 Ukrainian population census, 67.5% of Ukraine's citizens consider Ukrainian to be their mother tongue, versus 29.6% of citizens who consider Russian to be their mother tongue. And while an outsider may consider this breakdown to be a good representation of language usage in Ukraine, these numbers are rather misleading.
The reality is that language usage in the Ukraine is more "grey" than black and white. Ukrainian tends to be spoken at government institutions, official state events, universities and schools. Russian is often a more practical language in business and commerce. Even in these environments, however, there is no strict rule. The majority of the population understands both languages, so its not uncommon to see a conversation on the street where one participant uses Russian, the other Ukrainian (and vise versa). A good example (if you have some knowledge of either language) is to watch a talk show or game show on Ukrainian television. It quickly becomes evident that Russian and Ukrainian are regularly used in the same conversation.
Often you will even hear elements of both languages coming from the same speaker. While grammar teachers may consider this improper (to combine the two languages together), many people speak such a dialect. This form of Ukrainian, that is heavily influenced by Russian, is known as "Surzhyk". And while its common for the Ukrainian language to be influenced by Russian, the same is not as common in reverse. As a result, you are more likely to hear a "cleaner" form of Russian spoken than Ukrainian, unless you are traveling to areas in the west where a "pure" dialect of Ukrainian is more common.
Of course, the usage of Russian and Ukrainian is quite divergent depending on the region of Ukraine. On one extreme, a very small percentage (less than 5%) of the population uses Ukrainian in Crimea and cities in the far east - Mariupol, Donetsk and Lugansk. These cities are predominantly Russian speaking. On the other extreme, a very high percentage (greater than 90%) of the population uses Ukrainian in western cities like Lviv and Ivano-Frankivsk. Other cities fall somewhere closer to the mean, depending in large part to their proximity east or west of the Dnieper River. Finally, its important to remember that these figures are just estimates since, when asked, many individual Ukrainians can't even say definitively which language they use on a day-to-day basis (since they are using both).