Have there been such an attempt made to make the comprehensive list of all New Testament scrolls ever found? Have there been any attempts made to make a comprehensive list of all scrolls or pieces of scrolls of the New Testament (in original languages) that have ever been discovered by archeologists?
For the New Testament, yes. Though Wikipedia may not be a "scholarly" source I find it good for this sort of thing.

http://en.wikipedia.org/wiki/Biblical_manuscript#Listings

Also, in at least the UBS and NA, there is a list of manuscripts used to compile the "Greek New Testament." I think that the BHS contains something somewhat similar for the Hebrew Bible.