I've recently enjoyed reading the online debate between the atheist writer Sam Harris and Catholic blogger Andrew Sullivan at: http://www.beliefnet.com/story/209/story_20904_1.html
At one point Harris asks Sullivan what kind of evidence he would require to abandon his belief in God; something that Sullivan doesn't subsequently address.
As a Christian myself, I thought I would give my own answer to Harris's question here by listing five scenarios, any one of which I would consider strong enough to falsify my belief in God:
1. If the Universe were shown to be eternal - however the vast majority of scientists accept the Big Bang hypothesis which says that the universe had a beginning (around 13.7 billion years ago). Many scientists (including Einstein) were originally extremely unhappy with the theory that the universe might not be eternal, yet all the evidence indeed points to it having had a beginning.
2. If the properties of our Universe were shown to be non-significant - I'm familiar with the argument that even if our universe had only a (say) 1 in a million chance of existing in the form it does, it doesn't demonstrate anything significant about our universe.
The argument goes that it is equivalent to a person throwing a ball in a field and then arguing that the blade of grass it lands on is special because it had only a 1 in a million chance of being landed upon. However our universe is peculiarly capable of complex, intelligent, self-aware life - dependent on many extremely low-probability factors - so that the correct analogy would be if the ball landed on a blade of grass which was coloured blue while all the others were green.
3. If the Universe were shown to be only one of an infinite number of 'multiverses' - So far, we have zero evidence for any universe but our own.
4. If our Universe were shown to have other complex, intelligent life forms without religion - Although decades ago the belief among scientists was widespread that our universe was teeming with intelligent life, currently we still have no evidence whatsoever for the existence of any other intelligent life in the universe. Some scientists have calculated that the probability of such life existing is in fact close to zero. Humans may well be alone in the universe.
5. If it was shown that our ideas and beliefs are exclusively the result of biological and cultural processes entirely beyond our control (and therefore their content immaterial) - or, to put it another way, if it were shown that there is no such thing ultimately as 'Truth'.
However one such well-publicised attempt - Memetics - has largely failed; its Journal ceasing publication in 2005 and many of its advocates having moved away from it.