Based on simple probability, I do believe that alien life exists. The universe is so vast that I think it would be simplistic to think we are the only life in the whole universe. It doesn't necessarily mean it is advanced or smart alien life and it could very well be life very different from what we understand life to be, but I feel very certain about it.
I know that such a discovery will not be made in my life time, which saddens me in a way, but future generations will be lucky enough to finally answer this age-old question and I can only imagine what an exciting time it would be.