Ask a scientist, and the answer is, unsurprisingly, no. Ask a politician, and the answer is yes. Ask an engineer, and they’ll laugh that the question is even being asked, and go back to making something useful.
Of course, this is a simplification. Many scientists fully believe that it’s proper for science to offer a return on its investments. There may even be some politicians that make rational, scientific decisions on policy based on available evidence (there’s certainly a calling for it among the Behavioural Insight Team in the Cabinet Office ), though we see few of them here in the UK. There was, in April 2010, a “Science Party” who stood for election in Bosworth, but nothing much came of it.
On the whole, especially in the UK, there’s a perception that science has no place in government; the zeitgeist is that science is cold, clinical, detached and incapable of appreciating the human element to the problems we face today. This attitude has led to the current government shrinking the science budget for the first time since 1986. It’s an easy target, and one that some people won’t miss. So, the rather trivial answer to the question of whether science should justify itself is that it had better shape up and do so anyway if it wants to get its pocket money.
Science, despite what new-age hippies and “Big Pharma” conspiracy theorists say, is generally regarded as having a positive impact on economic growth, regardless of individual experimental outcomes. The question, as is often the case in politics, is whether the return on the investment is a net positive once funding and subsidies have been accounted for. Many scientific , once the recent academic cuts were announced, came out in favour of science,  and no further real-term cuts have been made.
Still, the fact remains that the UK scientific spending lags, at 0.65% GDP, behind the G8 and European averages of 0.8%, putting increasing pressure on scientists in Great Britain to either get funding from private sources, or to squabble for resources within growing fields offering ever-more avenues of interest. Whilst scientists may believe that the pursuit of knowledge is a goal in itself, economic return has, and will continue to be, a carrot-on-a-stick for those who have a more pragmatic view of governmental spending.
Other arguments aim towards pointing out that scientific funding leads to very real benefits. Usually these benefits are medical in nature – who doesn’t love new methods of noticing and battling cancers? – but other applications appear, from 3-D printing to quantum computing. These new technologies appear as if from nowhere, in fields that couldn’t have predicted them even a few years beforehand. Whether this is a sign that we need more funding to spot them sooner, or less to avoid unnecessary dead-ends, really falls down to personal analysis.
 http://www.telegraph.co.uk/science/science-news/8052735/Science-funding-cuts-will-cost-UK-economy-billions.html, http://www.bbc.co.uk/news/science-environment-23065763, http://www.huffingtonpost.co.uk/bob-ward/science-funding-cuts-british-antarctic-survey_b_1931681.html