There are "alarm indicating fuses". **broken link removed** They come in various different forms and require special fuseholders. The alarm portion can activate switches and thus you can have what you want.
They are typically used in telecommunications.
Breakers can have sense and trip contacts in them as well.
One of the simplest in principle that was already discussed is low current light ACROSS the fuse, whether it be a LED or Neon bulb and resistor. The circuit needs to be carefully thought of too. In general, the circuit fails shorted, so there is a path for the fuse to light when the fuse blows. Light glows when fuse blows.