PBS announced (end of May press release)that it will close down the scheme as of December 31, 2005.
Nils Hilbard, director of payment cards in PBS A/S states among others that:
"The perspectives of having an electronic purse has not attracted enough merchants to accept Danmønt. The limited user possibilities have limited the Danes' interest in having a Danmønt card. We have therefore decided to close down the scheme from 31 December 2005. Cards can still be acquired, used and loaded until the end of 2005."
Dankort (the debit/credit-card) will fill the gaps that Danmont leaves. And I'm sure some other payment mechanisms (contactless) may enter the scene some day.