I think it emphasizes that the person did not think aloud or express the view to anyone else. [The reflexive is commonly used for emphasis: I, myself, didn't like the spaghetti at that restaurant.]
Redundant and casual, but useful. "I thought" is more clinical. "I thought to myself" implies contemplation or musing of a thought that will not be expressed.
"I thought he was going to shoot me."
"That dress looks horrible on her," I thought to myself.