Parakeets, cockatiels, mynah birds, ravens, and some parrots are all able to mimic the sounds of human speech -- a fascinating and uncanny capability that has earned many of these birds great popularity as pets. Of course, the birds aren't actually speaking or using their tongues to form the words, but as a result of consistent exposure and an instinctive tendency toward mimicry, they remember the sounds and emit them using an organ in the back of their throats called a syrinx.
According to pet expert Marc Morrone, if you own one of these birds, it is possible to coax them into "speaking" by repeating a word or phrase as often as possible, but you may experience varying degrees of success, depending on the individual bird -- their abilities can differ significantly even within the same species. In general, you'll enjoy the best results if you obtain the bird while it's young and make it feel as if it's a part of the family. Most importantly, remember to be patient; it can take anywhere from a few days to a month for your pet to speak.
Learn more about talking birds at Pet Bird Report.