Is immortality achievable by humans?
As far as mythology, religion and spirituality are concerned, yes, either physically or spritually. For example, in Christianity, after death, the human's conciousness continues to exist. In Greco-Roman and Norse mythologies, an apple-tree is mentioned which produce golden apples that if eaten, can make the eater live forever. Also,there is the belief that after death we go to different bodies, so although someone believes he is 42 years-old he might actually be 346, meaning that he lived previous life(s) in different incarnation(s).
As far as science is concerned,there are attempts to make human life longer, and there are many who believe that in a few years science will suceed in expanding our lives. However, immortality, as to live forever, is a huge concept, and there is no serious scientific proof that this is possible, at least for know.
Soon technology will be so advanced that just as the chip doubles processing power every 18 months, so too will the intelligences improve itself. Soon this intelligence of A G I for artificial general intelligence will refine the process of creation to improve itself each time to the extreme. Some believe that it could focus on re organizing the material in the universe to more efficiently use of space thus allowing further expansion.
By that time we will have found a way to "join" as if it hasn't already happened.
Link for the scientific speculation on the subject with numbers and more facts
The Singularity Summit 2009 > Program