What don't we know? In a 2005 effort, Science Magazine took a stab at formulating 125 big questions for which some answers might be found in the next 25 years. The first 25 questions are here (PDF), the next 100, here.
A lot can change in four years, of course. And an answer to the question of "whether we're alone" might not talk today about SETI, but reference instead the recent launch of Kepler. By broadening the question to ask whether we're the only life in the cosmos, the answer is almost certainly no. If the recently launched mission is successful, other terrestrial, Earth-sized worlds in the habitable (water likely) zone of other stars may well be reported over the next three years.