What are some unusual places copper is used?

Not that this will help with your scrap metal project, but I learned that many metals are dipped in Copper (Copper cyanide) in the process of chrome plating them.  It acts as a binder and it is a very unusual place that copper is used. http://en.wikipedia.org/wiki/Chrome_plating If you want your kids to earn some real money in scrap metal; there is a fair amount of platinum in catalytic converters.  ;)

I worked for a copper and brass company back in the 1980's. We produced copper wire that were formed into rivets for the Statue Of Liberty Restoration project during that time. Copper rivets were use to fasten the copper sheathing used for her robes. Perhaps not unusual as we supplied over 80 different copper alloys used in thousands of market applications, but this was perhaps one of the most memorable for me.  The copper wire was donated by the company https://en.wikipedia.org/wiki/Restoration_of_the_Statue_of_Liberty

I save romex cable and THHN wire for this very purpose.  You can take it in without removing the sheathing and it's still worth quite a bit.  It's often thrown away during construction and remodel projects because people either don't know what they can get for it or they don't want to bother.  If you know an electrician or building professional, ask them to let you know when they have wire scraps available.  Or just drop by a job in progress and ask the person in charge if you can raid the dumpsters or trash piles. Others already mentioned plumbing. Also, some old satellite dishes are made from aluminum; if you dismantle one of those and take it in it's worth about fifty bucks, if my memory serves me right.  They can be a little cumbersome to transport though.

This market for copper has caused some problems at job sites in the metro-Detroit area.  People steal copper pipes from construction sites.  The upside is that there are not so many construction sites in Detroit these days, but it's a problem for the ones that exist. The same has happened for aluminum -- sometimes used as an alternative to copper for wiring.  Houses have been stripped of aluminum siding for the scrap value.  Kind of like Hansel & Gretel taking shingles off the gingerbread house...

Here are some odd ones: Treatment of lumber for homebuilding. The baseboards in any basement must be resistant to rot and mold because of the sheer probability that there will be water in the basement.  Some of the wood used is naturally resistant to mold, but some of it is pressure-treated with some copper-containing chemicals.  The copper content makes it inhospitable for bacteria and fungus, which makes it highly resistant to mold and rot. In metals identification. One of the most popular methods for metals identification is X-Ray Fluorescence Spectroscopy -- popular primarily because it's really accurate for metal sorting and can be done with a handheld instrument.  For identification of heavier metals, the x-ray tube used has a tungsten target, and its output is filtered with a thin sheet of copper so the radiation from the tube does not add noise to the radiation coming off the metal to be identified. In industrial vacuum systems. I don't know all the reasons why copper is used in them, but apparently its softness allows it to form hermetic (non-air-leaking) seals at joints better than other things. In integrated circuits. Actually it's pretty obvious.  Copper is a much better conductor than the aluminum that was formerly used to make interconnects between different sections of chips.  Using it allows you to have lower resistance between sections and make denser patterns.  It's necessary to make faster, lower-power chips.  But the copper can't be allowed to touch the silicon, or else it will completely ruin the electrical properties of the silicon.  There's a lot of care taken to make sure that the silicon itself is never exposed to copper. Sorry, these aren't places to harvest copper from, but they're interesting uses for copper, and perhaps might give a little extra perspective.

I would say the most unusual place copper is being used has to be the penny.  It is practically worthless after all, and many countries have got rid of it (or some version of it) altogether!  Though I guess they are predominantly zinc. Fortunately Canada is phasing it out - finally. http://blogs.canada.com/2012/05/03/final-canadian-penny-gets-stamped/