thedoclc said:
If we go by the "own merits, doing what they're made for," per the OP, the rapier and other smallswords are absolutely, positively missing from this list. (I'd also consider weapons which are meant to be used together as a single "weapon," and that would put hoplon + dari + xyphos and scutum + gladius + pilum very close to the top of the list. So I'll treat it as "rapier + main gauche or buckler or pistol".)
The rapier was not designed as a military arm nor as an armor breaker. The reason was because at the time of its development, armor was very, very quickly disappearing from warfare and civilians don't use armor. The rapier was never intended as a military weapon; it was a sidearm for civilian use. These objections aren't well-suited to this list.
What the rapier did do was overcome the cut-and-thrust weapons of its era handily, eventually forcing anyone who wanted to survive a sword fight to adjust what they used. Cutting weapons were very quickly replaced in Europe because hold-outs who rejected the rapier and linear fencing died in droves. A rapier's lunging attack and ability to disengage underneath or over an opponent's hands made it extraordinarily difficult to stop and kept someone using a rapier at a safe distance. Paired with a main gauche and buckler, it retained defensive capability even in a committed attack. If an opponent with a heavier weapon attempted to parry, the blade could be slipped under their weapon with a swift wrist movement and the same attack continued. And while the wounds dealt were hardly the spectacular gorefests of Deadliest Warrior, let's remember a popped lung was just as fatal as decapitation back before modern medicine, and a hell of a worse way to go.
Estimates of the number of nobles killed by these swords gets into the very high tens of thousands. How many common folk were killed in the street or by highwaymen with these weapons I can't imagine anyone can tally.
You clearly seem to have a lot of knowledge about the rapier and its application, how it works, the innovation of the Capo Fero lunge, the disengage, the sheer fucking speed of the thing. Not too much I can add. Armour was not entirely absent when it was used. You still had the buckler and sword combination holding out in England for a while, light brigandine had been worn by nobles concerned for their safery for some time (goes under the puffy outfit) and still lasts into the Renaissance. Pikemen and equipping them with some armour lasted for a while and depends on time and place. Go east and the Ottomans and Arabs still used lamellar, leather, leather-scale for a damn long time. Brigands and highwayman would equip themselves with whatever they could get away with and afford.
The rapier is not a heavy armour puncturer (just go round and find the opening), you would want a pick or a polearm for something like that (bec de corbin perhaps, or spetum or awlpike). Then again the tuck or estoc is a two-handed rapier designed to pierce armour
http://www.myarmoury.com/feature_euroedge.html
I find the Spanish and German basket-hilt rapier designs the most pleasing, combining buckler and sword together, as the epee in fencing illustrates. Course I also find some of the European one-handed falchions quite nice and look to be useful and used more amongst Europeans then we might think, but then again, the Swiss also made two-handed sabres which look a lot like the lauded katana).
http://en.wikipedia.org/wiki/Falchion
http://bjorn.foxtail.nu/h_conyers_eng.htm
http://www.myarmoury.com/review_lut_10006.html
Did you know, despite a lot of criticism, some cavalry units actually went for rapiers over sabres or cavalry swords? (Cohen 2002). Some generals said it would never work and would break, others insisted it was just fine in the field. Suppose it could be used like a swift light lance in a way.