This is a treacherous question to ask, and a trivial one to answer. Treacherous because the shoals between the written lines can be navigated by some to the conclusion that truth and religious belief develop by the same means and are therefore equivalent. To those unfamiliar with the process by which scientific hunches and hypotheses are advanced to the level of verifiable fact, and the exacting standards applied in that process, the impression may be left that the work of the scientist is no different than that of the prophet or the priest.
Of course, nothing could be further from reality.
The whole scientific method relies on the deliberate, high magnification scrutiny and criticism by other scientists of any mechanisms proposed by any individual to explain the natural world. No matter how fervently a scientist may "believe'"something to be true, and unlike religious dogma, his or her belief is not accepted as a true description or even approximation of reality until it passes every test conceivable, executable and reproducible. Nature is the final arbiter, and great minds are great only in so far as they can intuit the way nature works and are shown by subsequent examination and proof to be right.
With that preamble out of the way, I can say that for me personally, this is a trivial question to answer. Though no one has yet shown that life of any kind, other than Earthly life, exists in the cosmos, I firmly believe that it does. My justification for this belief is a commonly used one, with no strenuous exertion of the intellect or suspension of disbelief required.
Our reconstruction of early solar system history, and the chronology of events that led to the origin of the Earth and moon and the subsequent development of life on our planet, informs us that self-replicating organisms originated from inanimate materials in a very narrow window of time. The tail end of the accretion of the planets—a period known as "the heavy bombardment"—ended about 3.8 billion years ago, approximately 800 million years after the Earth formed. This is the time of formation and solidification of the big flooded impact basins we readily see on the surface of the Moon, and the time when the last large catastrophe-producing impacts also occurred on the Earth. In other words, the terrestrial surface environment didn't settle down and become conducive to the development of fragile living organisms until nearly a billion years had gone by.
However, the first appearance of life forms on the Earth, the oldest fossils we have discovered so far, occurred shortly after that: around 3.5 billion years ago or even earlier. The interval in between—only 300 millions years and less than the time represented by the rock layers in the walls of the Grand Canyon—is the proverbial blink of the cosmic eye. Despite the enormous complexity of even the simplest biological forms and processes, and the undoubtedly lengthy and complicated chain of chemical events that must have occurred to evolve animated molecular structures from inanimate atoms, it seems an inevitable conclusion that Earthly life developed very quickly and as soon as the coast was clear long enough to do so.
Evidence is gathering that the events that created the solar system and the Earth, driven predominantly by gravity, are common and pervasive in our galaxy and, by inductive reasoning, in galaxies throughout the cosmos. The cosmos is very, very big. Consider the overwhelming numbers of galaxies in the visible cosmos alone and all the Sun-like stars in those galaxies and the number of habitable planets likely to be orbiting those stars and the ease with which life developed on our own habitable planet, and it becomes increasingly unavoidable that life is itself a fundamental feature of our universe ... along with dark matter, supernovae, and black holes.
I believe we are not alone. But it doesn't matter what I think because I can't prove it. It is so beguiling a question, though, that humankind is presently and actively seeking the answer. The search for life and so-called "habitable zones" is becoming increasingly the focus of our planetary explorations, and it may in fact transpire one day that we discover life forms under the ice on some moon orbiting Jupiter or Saturn, or decode the intelligible signals of an advanced, unreachably distant, alien organism. That will be a singular day indeed. I only hope I'm still around when it happens.