If you look at the WW2 map, Hitler invaded almost everywhere around Turkey but didn’t even touch Turkey. Why?
German Turkish non-aggression pact, perhaps.
Yeah, having one of those kept him out of Russia, too. 
Hitler didn’t really attack everywhere around Turkey. 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.
Turkey could have helped him flank the USSR–though if he’d done Barbarossa right he wouldn’t have needed any geographic help.
Turkey was a useful neutral and provided Chromium in trade to the Germans. They also enabled some small indirect trade for Germany with the Allies. 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. So a neutral Turkey offered Germany some advantages. And a belligerent Turkey offered another 40 odd divisions of difficulty. Not much of problem by themselves, but an unfortunate addition while the war raged with Russia. So the cost / gain ratio was never favorable.
But Turkey might have had cause to regret their neutrality if the Germans ever won in the East. It is hard to imagine that Hitler would have let them be. They would have eventually either have to choose to join the Axis or would have been invaded.
Further to what Bartman says above, Turkey is also quite difficult terrain for any would be conqueror.
Indeed. Aside from the mountainous terrain in Asian Turkey, I wouldn’t envy the Axis trying to force a crossing of the Bosphorus.
You 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.
He was vegetarian.
(Well, maybe.)
Which is exactly why the also allied with the Italians and Japanese…oh wait.:rolleyes::dubious:A
But Germany allied with Ottoman Empire, not with Turkey. And, founders of Turkey strongly opposed Ottoman Empire. As far as I know, Ataturk, when he was a military officer in Ottoman Empire, was reluctant to join WW1. According to him, if Ottoman Empire had to join WW1, then the ally should be the British. Enver Pasha, with whom Ataturk disagree, was the architect of the Ottoman-German Alliance. So, I don’t think Turkey had been a stalwart ally.
Oh, that’s good. Very Good! 
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.
He may have been stupid, but he wasn’t that stupid.
They sure seemed stalwart at Gallipoli.
That’s only natural when it’s your own country being invaded. Kaiser who?
Perhaps he was concerned that he couldn’t defeat their air force (“As Gott is my vitness, I thought Turkey could fly…”)
Kaiser Bill. You know, the guy with the batman.
Oh, you wanted something relevant?
Could Hitler have gone south? An enlightening previous thread.
No. I don’t think so. Gallipoli War was to defend themselves. It indirectly helped Germany, perhaps. But I think I can safely say the first priority in Gallipoli War was to prevent the Ally forces from reaching Istanbul through Canakkale.