I was just curious about how wide a rapier blade could become. The widest rapier blade that I've seen is 1 1/4" wide and has two sharp cutting edges as well as a sharp point.

Are there any blades that are wider than 1 1/4", or would these swords be classified as a Cut-and-Thrust sword, rather than a common rapier blade used for thrusting?

"Rapier" is really a fairly non-informative term used to describe both thrusting-oriented civilian swords of the late renaissance period, and the geometrically inspired style of unarmoured combat that was commonly practiced with the sword for self-defense and (frequently unsactioned) dueling during the same time period. While an elongated and well tapered blade and complex (as well as frequently ornate) hilt design are often considered indicative of a "rapier", realisitcally any sword offering a straight, double edged blade with a servicable point for thrusting and a weight and balance suitably nimble to easily manipulate with one hand without relying on additional armour for defense should well suffice for the style of combat. In general, longer and more slender blades were preferred by styles more oriented purely to the thrust, and broader and shorter to those that used the cut with more regularity; heavier to those used militarily and lighter tro those used only for personal defense and/or duelling; however, the ongoing debates of cut-and-thrust sword vs. rapier vs. riding sword vs. sidesword vs. edge-sword vs. (insert other awkward translation to english here) seem to much more frequently be semantic definitions than practical ones. In my (perhaps limited) observation, historically "rapiers" and "rapier hilted swords" seem to have ranged from nearly edgeless examples less than .5" at the forte to heavier and more cut-oriented "riding swords" cut-and-thrust swords" or "sideswords" ranging up to perhaps 1.75" at the widest point of the blade; I suspect the dimensions of blade width and lenght were much more a matter of personal preference, stature, in some (but by far not all) cases guided by professional advice from a master of fence, rather than strictly determined by the defined nomenclature of the sword itself.

As an intersting note, the term "rapier", and similar terms, seem mainly common in those countries that contributed the least and last to the development of this style of swordplay; in Spain and Italy both, the sword was more often simply called a sword regardless of the percentage of the time it was intended to be used for the thrust of cut.