I think it's really subjective. What a fun discussion to have, I'm sure lots of great opinions will come up.
Personally I think any fish that gets too big to fit in a standard size aquarium net borders monster status. It really depends though. I know I've personally been laughed at in an aquarium society for talking about my senegal bichirs as if they were big, as the people there had ornates, sand tiger catfish and redtail catfish. Those are kind of in a different league, hah! I kinda think they might have been compensating for something. I dunno, I just don't get the draw necessarily of seeking out a fish that will potentially hit 6 feet just for the sake of having a giant fish. It just so happens that many of the species I find interesting or aesthetically pleasing happen to get more than 6 inches though.
Really, for me, anything over about 5-6 inches is bordering on monster, depending on how powerful it is. Moving my dads goldfish indoors every winter (it gets -40 here every winter) isn't a huge deal, so they aren't monsters despite being about 9 inches. My Geophagus at 8 inches, however, is significantly more powerful. So are my bichirs at 7 inches. I don't know if a fish has to have a size restriction to get into the club necessarily, but it sure as hell doesn't hurt! I don't think anyone would argue that a 3 foot long fish is anything but a "monster" in this case but I would suggest a fish of even 6 inches could be deemed a monster if it's hard to manage, move or house.
An example: I don't think Koi really count as "monsters" even when they are big. I do think Exodon paradoxus counts as monsters, even though they are comparatively small (4 inches or something like that)
