The European Center for Nuclear Research (CERN) is the place where the World Wide Web was developed. Even the uncultural people who don't care about the existence of the Higgs boson or the superpartners may have noticed one of the by-products of high-energy experimental physics, namely the web.
Despite some rumors, Al Gore did not invent the web. The only discovery in computer science that Al Gore has made are algorithms. :-) Despite the contributions of the unsuccessful 2000 presidential candidate to computer science, you should keep in mind that most websites start with Dubya Dubya Dubya.
The Large Hadron Collider should start operations in 2007 and it will require many gradual technological advances to occur. Look at this article:
In this article, you can remind yourself about the immense amount of data that CERN will generate and that will have to be analyzed. Even if the people do not care about particle physics, experiments like the LHC represent a very natural playground to improve technology - such as grid computing - that can become useful in many other contexts in the future. Of course, these results are not the goal of particle physics but rather a by-product; but they are another reason why people may find investments to pure science - and high energy physics in particular - to be a good idea.
When I mentioned the LHC, there is one more LHC associated with CERN: "Les Horribles Cernettes" were a music band whose photograph became the first image ever displayed on the World Wide Web. Their 9 songs were so excellent that they have even be remade by your humble correspondent (lhc-*).