Gonna borrow your post, Tiberius, as it gives me a good springboard. First, I do agree that it's often foolish to take the unknown and ascribe "God Did It" to it.
But what is a "Higher Power"? Often taken as "Mysterious Sky Daddy" a la Modern Christianity, it's really nothing more than things that are greater than us. For myself, and in my beliefs, I recognize and give offering to the landvættir (wights or spirits of the land) as without the land I would have nowhere to live, and nowhere to grow crops or gather water for sustenance. They are greater than me. I honor my ancestors, because I am a reflection of my ancestors. I am the current sum of all that they were, and they are greater than me. And, when the time is proper for it, I honor my gods. I hail to Thor, Loki and Odin as the thunderstorm passes over, I honor Freyr and Sif in the harvest season. These forces and these events are greater than me, in both strength and importance for all.
But a lot of other things are of my own making and skill, and often require no thanks given to anything or anyone. My skill in artwork, my intelligence, my wisdom through experience. For these things I have only myself to credit, and those who have taught me various skills. I needn't thank a god for every breath I take or meal that I cook, or worse still for the skills and services of others (such as doctors). I find it insufferable when others will demean the works of others and thank their god for what human hands gave them...