Crows are likely on par with chimps and dolphins for intelligence by creating their own tools in the wild and other intelligent behavior (language, facial recognition, passing on knowledge).
Parrots such as African Greys and cockatoos are right up there too with problem solving abilities. I know cockatoos can be trained to "pick locks" and then pass on the knowledge to other cockatoos.
http://news.bbc.co.uk/2/mobile/science/nature/8631486.stm
https://www.psychologytoday.com/blog/avian-einsteins/201207/...
http://www.nwf.org/news-and-magazines/national-wildlife/bird...
https://youtube.com/watch?v=BGPGknpq3e0
http://www.pbs.org/lifeofbirds/brain/
https://en.wikipedia.org/wiki/Alex_(parrot)
http://www.bbc.co.uk/nature/23150941
https://www.google.com/search?q=canuck+the+crow&ie=utf-8&oe=...
Not necessarily true.
http://blogs.thatpetplace.com/thatbirdblog/2011/06/10/do-par...
Edit: fix link
I know much more about birds than primates, so correct me if I'm wrong. Birds tend to be around people in captivity much more than monkeys, so guessing that may be part of the reason as well.
[1] http://www.news.cornell.edu/stories/2011/07/parrots-learn-th...