The most noteworthy effects IMO, would be:
1. Germany gaining access to the oil and other natural resources of the Middle East and North Africa.
2. Denying or at least sharply hindering British access to India, and it's capabilities to bomb the Ploesti oilfields of Romania.
3. Freeing up of Axis manpower and materiel in the region for more constructive purposes.
4. The prevention (if the Axis maintains it's hold on these territories) of all future Allied aggression from the region against Mediterranean targets, and the closing of a front to the benefit of the Axis.
5. Possible deportation of sizeable numbers of Jews to Palestine - I heard a bargain resembling this was brokered between the Reich and Zionists, though obviously never came to fruition.