"Futilitarian" is an adjective or noun for the belief (or a person who holds it) that all human striving is useless. The word is a blend of "futile" and "utilitarian" according to A.Word.A.Day and Merriam-Webster, though the American Heritage Dictionary says it's formed from "futility" and the suffix "-arian." The first usage I can find is in Cyril Connolly's 1938 "Enemies of Praise."
Reverend Don Beaudreault of the Unitarian Universalist church describes futilitarians as "folk who had given up the expectation that humanity was progressing, believing, instead that life was just a series of stops and starts and was really going nowhere; that life was futile." The idea of futilitarianism is sort of an offshoot of existentialism and nihilism, but in philosophy, the word tends to be written about largely by people who wouldn't consider themselves to be futilitarian and are trying to refute the position, often by arguing that even if people are not created for a purpose, the purposes that they create for themselves are meaningful. Bertrand Russell and Samuel Beckett are among those whose views have been called futilitarian.
"Futilitarian" is also used in a medical context to describe those who believe that care which prolongs a patient's life without making them any better (such as during persistent vegetative states, etc.) is not worth doing. This is a controversial position, and the label "futilitarian" seems to be more commonly used by those who disagree with it.
Sources:
http://www.wordsmith.org/awad/archives/0803
http://www.m-w.com/cgi-bin/dictionary?book=Dictionary&va=futilitarian
http://www.bartleby.com/61/61/F0376100.html
http://www.infoplease.com/dictionary/futilitarian
http://www.fusmadison.org/sermons/2004/2-1-04_humanist_heritage_2_sgp.shtml
http://uusara.lunarpages.com/minister/don62.htm
http://www.wendi-milner.com/blog/archives/2003_08.php
http://www.broadwaybks.com/si/1619.html
http://www.braintreeusedbooks.com/si/024392.html
http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=10974983&dopt=Abstract
http://www.rawfoodinfo.com/articles/art_medicalfascism.html
http://www.cmaj.ca/cgi/reprint/160/6/869