This is probably the main point most people make when arguing against space exploration, despite it being heavily flawed. The technological, economic, and political gains of achieving ambitious goals in space exploration such as the Apollo missions gives it by far the best return on investment of any government program and there is no reason to doubt that a mission to Mars would be any different.
We've gone into more details about each of these areas below for anyone who believes investment in space is a waste of money and has no impact of things here on Earth:
Technology - There have been countless technologies and products that NASA and the Apollo missions have given us (See here for details), some of the main ones include water purification systems (benefiting people all over the world who need affordable, clean water), Memory Foam, Enriched baby food, Portable cordless vacuums, Freeze dried foods, Enhanced Solar Energy Cells, Firefighting equipment, Aircraft anti-icing systems, and around 1650 other spin-off products in the fields of computer technology, environment and agriculture, health and medicine, public safety, transportation, recreation, and industrial productivity. And that's just NASA alone, if you take into account the other products you get from space, you have GPS on your phone and in your car, Google Maps, Satellite Television, Satellite Phone and Internet Access almost anywhere in the world, and Weather and Climate Satellites providing essential warning in numerous disaster events. If everyone decided to fund projects here on Earth over attempting to explore space, none of these products would even be possible, and there are still endless possibilities for the future.
Economic Gain - It has been estimated that for every $1 the U.S. Government invests in space development, it returns $7 in economic activity. Yet since 1994 NASA has received less than 1% of the federal budget. In 2010, it was $18.7 billion out of the $3.55 trillion budget. Even though increasing any government spending in any area is not ideal, and while in the long run it is hoped that the private sector will fund the vast majority of space activity, in the short run the government could substantially speed up the process by embarking on challenging ventures such as a mission to Mars, as these create the most technological spin-offs (like the ones stated above) for the private sector (Investing in cheaper alternatives to rockets for getting into orbit such as a Space Elevator, is another project which would significantly boost private investment in space). It's this sort of investment in technology to overcome the challanges of space which can create new markets, new businesses, new products and new highly skilled jobs for the struggling U.S. and Western economies in both the short and the long run. Imagine what could have been achieved if even just a fraction of the trilions of dollars spent on bailouts, wars and stimulus packages was spent on kickstarting a thriving space industry, we could have multiple colonies on the Moon and on Mars along with new affordable ways of transporting the average person into space or mining asteroids for a profit, all of which would provide massive economic opportunities.