I live in the United Kingdom for a start, which has not been involved in any recent genocides. You mentioned a genocide 20 years ago, are you refering to the attrocities committed by Serbia during the Bosnian war? As for Turkey and Armenia there is a lot of debate about how many actually died during the First World War. Also Turkey did not exist as a country until after the Treaty of Sèvres, one of the three treaties that ended the First World War resulted in the desolution of the Ottoman Empire. The other treaties I refer to here are the Treaty of Versailles, in which Germany lost territory to neighbouring countries and the Trianon Treaty which decimated Hungary.
As for the Armenian-Azerbaijan situation both those countries were absorbed into the Soviet Union and during the next seven decades populations were displaced, certain ethnic groups expelled and other groups encouraged to settle in occuppied territories. You may remember the brief war between Russia and Georgia a few years ago. This was caused by Georgia trying to retake control of two regions where ethnic Russians had become the majority. Georgia initially indended to boycott the Eurovision Song Contest which was being hosted in Moscow, before submitting Put-In Disco by Stephanie and 3G which was banned as it allegedly insulted Vladmir Putin! The Baltic States also have large Russian minorities, many of them being denied full citizenship unless they pass the local language tests.