Use them when buying things in shops. If you buy something that is, say, 806 yen, hand over 1,006 yen and get 200 yen change rather than handing over a 1,000 yen note and getting even more 1 yen coins in your change.
If you just want to get rid of them, put them in the charity collection boxes next to the tills in many convenience stores - or at the airport.

I had 500 once @_@. Though my bank took care of it, after counting it by hand 3 times .

Btw, camera film cases are ideal for separating coins, but I suppose people don't use them nowadays in this digital era.

//

Of course, you can say the same thing about any exotic coin including the 5 or 50 yen coins with the hole. Lots of people like them. Even Keith Richards.
http://www.rollingstone.com/news/coverstory/johnny_depp...

As for using them when paying for things, yeah I did. But I still wound up with over 60 of them when I was leaving Japan. They're like pennies in other countries once you have a couple of them they seem to multiply rapidly.