In Legends, there are some people/droids who did wear effective armor, but such armor was made out of rare and/or expensive materials.
There is an ore called cortosis which is resistant even to lightsabers. It was used in the armor for various troops and droids, such as C-B3 cortosis battle droids, purge troopers, and shadowtroopers.
C-B3:
Purge Trooper:
Shadowtrooper:
The C-B3 battle droid, for example, is a variation of the B2 battle droid, with the main difference being the armor. They were so effective that Palpatine believed they could tip the balance of the war for the Separatists and sabotaged them (recall that Palpatine was playing both sides of the war and had an interest in keeping the war "balanced" between both sides).
However, cortosis ore is rare, and the use of cortosis in armor is even rarer because of the Jedi:
Close at hand sat a stubby treddroid tasked with monitoring the progress of a mining probe that was sampling a rich vein of cortosis ore at the bottom of a deep shaft. A fabled ore, some called it -- owing to its scarcity, but even more for its intrinsic ability to diminish the effectiveness of the Jedi lightsaber. For that reason, the Jedi Order had gone to great lengths to restrict mining and refinement of the ore. If not the bane of the Order’s existence, cortosis was a kind of irritant, a challenge to their weapon’s reputation for fearsome invincibility.
Legends novel Darth Plagueis, p. 10 (emphasis added)
Note that cortosis has been depicted as having wildly different effects among conflicting sources. See Wookieepedia's "Behind the scenes" section in its cortosis article for more information about this.
Another ore that is resistant even against lightsabers is Mandalorian iron (called beskar by the Mandalorians). This ore can only be found in the Mandalore system, and many Mandalorians (but not all) used it in their distinctive armor. For example, this is Kal Skirata with his beskar armor:
Phrik is yet another material used to make lightsaber-resistant armor. It was used in the armor for Imperial dark troopers:
The orbalisk parasite could also be used to form armor capable of deflecting lightsabers (though this armor proved weak against electricity). However, the orbalisks had a tendency to grow over the entire body of their host and in doing so suffocate him. Consequently, the only known users of this armor are the Sith Lords Darth Bane and Freedon Nadd. Orbalisk armor proved particularly helpful to these Sith Lords as the orbalisks fed on the dark side of the Force -- Darth Bane's orbalisk armor made him stronger and allowed him to heal faster.
Darth Bane in his orbalisk armor (in the lower left corner with the red-bladed lightsaber and Force Lightning):
