If you look at the WW2 map, Hitler invaded almost everywhere around Turkey but didn't even touch Turkey. Why?
(OK. Hitler didn't really attack everywhere around Turkey. But Nazis came very close to Turkey, invading Greece)
1-) German Turkish non-aggression pact
2-) It was Italy that went into the Balkans and the Middle East and Hitler only reluctantly sent troops to these regions to back up his ally. Hitler was very Euro-centric - he had very little interest in acquiring territories outside of the continent. Germany was in Africa mainly to pull Italy's bacon out of the fire, as they were in the middle of being chased across the continent before the Germans showed up to save them, much to Mussolini's discomfort.
3-) Turkey could have helped him flank the USSR--though if he'd done Barbarossa right he wouldn't have needed any geographic help.
4-) Turkey was a useful neutral and provided Chromium in trade to the Germans.
5-) They also enabled some small indirect trade for Germany with the Allies.
6-) Unlike some other neutrals they also had a fairly robust military which for a while was actually being equipped by both the Axis and the Allies in an attempt to gain them as allies.
7-) Turkey is also quite difficult terrain for any would be conqueror. Aside from the mountainous terrain in Asian Turkey, Nobody would envy the Axis trying to force a crossing of the Bosphorus.
8.) We also have to remember that Hitler and the German people were, in part, acting out a revenge fantasy against their WW1 foes. And of course, Turkey had been a stalwart ally. Turkey sure seemed stalwart Ally to Germany at Gallipoli.
9-) There's also the fact that the portion of Turkey on the European side of the Bosphorus is so incredibly small that there was no point. It had no significant resources, and the territory wasn't strategically, or even tactically important. If he were to gain anything at all from attacking Turkey, he had to cross the Bosphorus. There's practically nothing on the European side to be worth pissing the Turks off, over. He was better off keeping them a 'friendly
but neutral' party.
10-) Hitler was a vegetarian