I don't think all crows are corrupted, only certain breeds like the Crebain.
That said, I think the crows that fly over my back yard are definitely spies of Sauron!
I don't think that crows were servants of Manwe in the same sense that the Great Eagles were, or in any real manner for that matter. The particular sub-species known as the Crebain do seem to have been easy for Saruman to sway into his service. It might be worth noting that the dwarves of the Company of Thorin did not think highly of the crows that dwelt near the Lonely Mountain either even though the ravens of Erebor were great friends to Durin's Folk.
There were neutral-good ravens in the Hobbit, but there were also crows that joined Saruman, just as there are good and bad men. Don't let their black feathers and digestive systems tough enough to eat carrion dissuade you, crows are some of the smartest and hardiest birds I've ever spoken with.
And just like Dwarves, they never forget a friend or an enemy.