All of the corvids (crows, jays, ravens, magpies, etc.--the entire Corvidae family) are highly intelligent. The Wikipedia article says they are the most intelligent of all birds, which I find a little hyperbolic after having lived with several species of psittacines (parrots, macaws, cockatoos, etc.).
Nonetheless, they are very bright and many species certainly rival the parrots in cleverness.
What tips the balance for me is that individuals of at least one species of parrot, the African Grey (Psittacus erithacus), have learned to communicate in words. Not just repeating phrases they hear, but actually putting words together to answer questions, such as "red key."
Some species of corvids, notably the raven, can repeat phrases.
Crows have been seen watching traffic patterns. Then when the light turns red, one places a large nut (too big for him to break) in exactly the place where a car will run over it after the light turns green. When it changes again, he retrieves his generous, now-edible, dinner.