Only recently reading about and seeing gameplay footage of the soon to be released game "No Man's Sky" has made me realize how unimaginably grand the universe is.
In the game a universe is procedurally generated and even though all players play in the same universe at the same time it is very unlikely to ever meet another player. In an interview with IGN one of the developers said that 99.9% of the in game planets will probably never be discovered. Also people have calculated that even by visiting one planet per second it would take over 5 billion years to discover all of the planets in the game.
Projecting this to the real world and assuming that the real universe is probably even bigger than the generated one, leads me to believe that we are not alone in the universe because even if there is a very small probability of life existing on a planet, if you repeat it an uncountable number of times even small probabilities virtually become a certainty. On the other hand while I am sure that other life exists, I dont think that we will ever meet or even find proof of it due to the grand scale of the universe.
Whether meeting an advanced Alien civilization would be a good or a bad thing is a totally different discussion.