Not including any other Middle Eastern rebels. Was the British Empire ever at odds with the Turks? This question is simply out of curiosity.
The Ottoman and Russian Empires were definitely in rivalry in the century before the First World War. Indeed, it is not too much of a stretch to describe Russia as the most consistent foe for the Ottomans in the nineteenth century. The Ottomans fought four major wars with the Russians in the nineteenth century (1806-12, 1828-29, 1853-56, 1877-78) and only one of these wars ended in an Ottoman victory, the Crimean War of 1853-56 when the British and French came to the aid of the Ottomans.
The two main geographic arenas of competition for the two empires were the Balkans and the Caucasus. Although Russian victories against the Ottomans were never as thorough and complete as St. Petersburg would have liked, the Russians succeeded in pushing out much of the Ottomans' influence in this region. There were also dreams among some Russian imperial expansionists of liberating Istanbul for the Orthodox faith and gaining control of the Straits. But one of the limits for Russian success against the ottomans were the other European powers. While many of them had no problems taking Ottoman territory for their own uses or turning them into client protectorates, as the French did in Mount Lebanon, the British in Egypt, or Austria-Hungary in Bosnia-Herzegovina, there was great alarm over Russia expanding too much at the expense of the Ottomans.
By 1914, the main arena for Russo-Ottoman competition was the Caucasus, as the Balkans were now largely independent of the Ottomans and were pursuing their own strategies vis-a-vis the great European powers. Both the Ottomans and the Russians sought to take advantage of national minorities on the other side of the Caucasus border in the hope that somehow their rival would face a national insurgency that would result in a client buffer state at the rivals' expense. This helped to contribute to a radicalization of nationalist politics in the fringes of both empires as well as a fear in both imperial orders of traitorous national minorities in their own empire. This was part of the reason why the First World War in the Caucasus was so brutal and at places took on the character of genocide. National minority politics of both empires on the Caucasus had become a tinderbox through decades of an imperial Cold War that it engendered worst-case scenario thinking about national minorities like the Armenians. As this imperial Cold War turned hot, more radical solutions towards borderland populations regrettably became more commonplace.
Sources
Bartov, Omer, and Eric D. Weitz. Shatterzone of Empires: Coexistence and Violence in the German, Habsburg, Russian, and Ottoman Borderlands. Bloomington: Indiana University Press, 2013.
Reynolds, Michael A. Shattering Empires: The Clash and Collapse of the Ottoman and Russian Empires, 1908-1918. Cambridge: Cambridge University Press, 2011.
Anything before WW1 please!