If there are no past and future lives, why should we practice Buddhism? If there are no past and future lives and everything ends at the moment of death. Why should we bother with anything at all?

Why would the Buddha teach for 45 years if all our problems are definitely solved at the moment of death?
There is no real difference between:

this current moment in life with future moments afterwards with Nirvana as the climax

and 

this current life with a string of lives afterwards with Nirvana as the climax.

The practitioner of the Buddha's teaching, done without ego, needs no future incentive.

Therefore,

We "should" practice to become enlightened and help others achieve enlightenment in this very life.