All astronomical objects are seen as they were some time in the past. The nearest quasars are about 780 million light years away. It probably still exists now, but you can't be sure. Wikipedia has a good article on the subject.
Do any quasars presently exist in our universe? Or are all the quasars gone?
Probably not. The current model for quasars is that they are powered by large amounts of gas and dust falling into a massive black hole. Once the black hole has cleaned out off all of the gas and dust, then you have no more quasars, and the former-quasar turns into a run of the mill normal looking galaxy.
Probably not. Quasar populations ramp up with redshift and none are known to exist locally. Hugely energetic source require hugely abundant fuel supplies. Ack, I just noticed twofish said the same thing.