Oil price changes have varying impacts on the financial indicators of global markets and economies. This study aims to explore the dependence structure between crude oil prices and stock market indices, as well as the exchange rates in a number of economies categorized with respect to their status as developing/emerging markets, and oil importer/exporter countries. Dependence structures in this study are evaluated in considerable depth using copula models. The broad time period covered allows the investigation of the effect of global financial crisis on the mentioned dependence structure. An additional feature of this study is the inclusion of 1 to 30-day analysis to capture the variation of dependence on duration change. To serve these aims, as well as ARIMA and GARCH models, various copula measures are used to illustrate the level of the association. Additionally, a special focus on the Turkish case is given to illustrate its sensitivity to oil prices. We find that exchange rates and stock indices of most oil exporter countries show higher oil price dependency, whereas, emerging oil importer markets are less vulnerable to price fluctuations. Considerable impacts were found for the global crisis and the continuing recent sharp decrease in oil prices. (C) 2016 Elsevier B.V. All rights reserved.