There are two reasons Rommel was able to get away with insubordination in North Africa in a way that few other commanders would have in any theater of war. First off, Hitler loved Rommel and considered him to be one of his most trusted commanders primarily because like Hitler, Rommel served in the first World War in combat, unlike most other German officers of his status, few other Field Marshals had the same sort of direct action experience. Hitler loved Rommel's aggression and drive and would lament that his other officers were not more like the Desert Fox. Hitler frequently complained that the officers in the high command lacked real combat experience and particularly after the war began to turn, Hitler would interfere and issue direct orders such as the famous "Stand and Die" commands given to Paulus at Stalingrad and Rommel himself at the second battle of El Alamein. The other reason Rommel was able to get away with ignoring direct orders was that he delivered victories. For example after arriving in Africa in February 1941 he was told to wait until the Afrika Korps was at full strength before attacking however Rommel took the 5th Light Division and routed the British at El Agheila in an extremely surprising advance both to German high command and the British. Hitler was thrilled at the initiative and loved this sort of thing. Sources: Knight's Cross: A Life of Field Marshall Erwin Rommel by David Fraser

Part of the reason why Rommel got away with what he did was Heinz Guderian's fault. Heinz Guderian, the father of German panzer doctrine, had Rommel as one of his commanders. He had a lightning advance through France, and outpaced the general attack so much that he was asked to stop by the High Command, and got away with it by claiming he was going to conduct a "reconnaissance in force." That basically meant he was going to take his tanks and run them as far as he could down the enemy's throat.

Rommel evidently learned some of this: when he was in North Africa, he was told to hold his position and wait for reinforcements, he instead attacked and pushed the British out of Algeria. His success in North Africa resulted in German command giving him virtually complete independence of command, which allowed him to run his tanks until he ran out of tanks.

One small factor in Rommel's seemingly untouchable nature was the way the doctrine of the Wehrmacht revered results above all else. While there was plenty of contention within the general staff throughout the war about the specifics of this plan or that (witness Case Yellow's many iterations), the one thing no one in the Prussian tradition could argue against was aggression that led to decisive results.

Rommel's hard-charging victories in France and then with his German and Italian troops in Africa bought him plenty of latitude with which to play the dashing hero (and he certainly loved doing that). His North African escapades were certainly assisted by the fact that for all his victories, North Africa received an incredibly miniscule amount of attention from the Wehrmacht compared to the Soviet threat to the east - enough to occupy British attention and keep the Italians from keeling over, but that was about it.

The German general staff was less than pleased with Rommel, though. In addition to his creative interpretation of orders, Rommel had a tendency to be rather vainglorious, a trait that endeared him little to other generals. He traveled with a personal press corps, and liked staging photographs for the benefit of his reputation back home. For all their misgivings about his attitude, though, his fellow generals had to admit that he produced results, and the Prussian military tradition inherited by the Wehrmacht glorified local commanders who acted on local information and produced results.

That last bit, "...and produced results," is the catch. Once Rommel lost at El Alamein, and especially after Operation Torch made maintaining his position strategic suicide, he fell out of grace quickly. Both Hitler and the Wehrmacht were swift in shaking up the North African command structure and reining Rommel in. Rommel's shattered forces retreated to Tunisia, where he found Albert Kesselring (the man who would later oversee the tenacious, but ultimately unimaginative, defense of Italy) in overall command.

Also, I like Rommel, I really do. But he was really hypocritical regarding the whole obeying orders thing. He wrote letters to his son telling him that he should obey orders immediately after they had been made because the commander wouldn't have time to explain. After discovering that his son, like himself, had a rebellious streak, he rolled his eyes and told him "Find another profession please". When Kluge came to Normandy, he summarily told Rommel that even he would have to learn to obey orders from now on. Rommel exploded and demanded to know when he did disobey orders! Like I said, many parts in that guy's brains seemed to work the wrong way.