What can a Runner do to trash ICE that is in play?
I believe the only three current cards that can trash ICE after it's installed are:


Parasite - program that reduces the strength of a rezzed ICE until it hits zero, at which point the ICE is trashed.
Forged Activation Orders - event that forces a Corp to rez an ice, or trash it if it can't (or doesn't want to) pay for it.
Kraken - event that forces the Corp to trash a piece of ice on a server that you choose (but can only be played if you've just stolen an agenda)


In addition, there are other cards (e.g. Imp, Demolition Run) that can trash cards that cannot normally be trashed - such as ICE - from HQ or R&amp;D, preventing them from being installed in the first place.

Edited to add:


False Echo - program that can be trashed when you pass an unrezzed ICE to force the Corp to rez it or take it back into HQ (which is a trash-like effect)
Forked, Knifed, and Spooned - run events that let you trash a piece of ice of a particular type if you break all subroutines on it