Currently, no such animal exists. With time and evolution and luck, potentially descendants of the great ape species could. Chimpanzees are fairly intelligent - they can learn some aspects of sign language - not enough to form coherent sentences but enough to communicate on a primitive level with humans. Dogs are intelligent also, and can solve problems, but lack the necessary digits to create a technological society. Maybe if they evolve another set of paws that eventually become hands?
Dolphins are VERY intelligent - not as intelligent as us, but not too far off. The US navy has trained Dolphins to detect and classify naval mines and even assassinate people (no joke, weapon-equipped dolphins are real, look it up). The stuff the Navy Dolphins can do is astonishing. But they couldn't create technology, being water based, lacking in hands and thumbs.
Elephants are fairly intelligent as well - they pass the "mirror" test, they have societies with rules and they have good memories (they have 'graves' where they return to to mourn their dead by rubbing their trunks over the bones). But again.... no hands, no real way to make complex vocal sounds meaning that their ability to create technology is virtually nil and their ability to form a complex, "real" language is limited. I suppose given a few million years of evolution, the elephants may develop highly sophisticated "dual" trunks that can manipulate objects much like how our hands manipulate the environment, and they may become a technologically advanced civilization.
It's all speculative of course. None of the current species on this Earth could ever become a technologically advanced species. But, with luck, some of their distant descendants might. Not very likely, though.