Sword
A sword was a handheld weapon usually made of metal, not unlike a large knife. Swords were far less effective than guns, but many races used them as their initial weapon. Even when it was superseded, the sword was still carried ceremonially as a symbol of honour. (TV: Revelation of the Daleks)
Irongron had his sword thrown from him by Linx. His men would later point their swords at the Sontaran. The Third Doctor himself successfully battled him with such a weapon. (TV: The Time Warrior)
The Doctor claimed to have learned sword-fighting techniques from one of Cleopatra's guards. (TV: The Masque of Mandragora) and to have practised with Richard the Lionheart, Cyrano de Bergerac and Errol Flynn. (TV: Robot of Sherwood)
Morgaine's forces, the S'rax, used swords in battle. The legendary sword Excalibur was the sword of King Arthur. (TV: Battlefield)
The Sycorax used swords to fight each other in their rituals. (TV: The Christmas Invasion)
Captain John Hart carried a Japanese sword with him, among other weapons. (TV: Kiss Kiss, Bang Bang)
Sontarans sometimes used swords. (COMIC: The Betrothal of Sontar)
On a minor note, "sword" and "words" are anagrams of each other, which helped the Second Doctor to turn a sword into a dictionary in the Land of Fiction. (TV: The Mind Robber)
The Ice Warriors made use of swords and battle axes when their sonic guns were jammed by the Eleventh Doctor's sonic screwdriver. (PROSE: The Silent Stars Go By)
A green-skinned race armed with swords attempted to invade Corbo, but the swords were useless against the devil-birds. (PROSE: The Devil-Birds of Corbo)
Swordfights
Ian Chesterton and the First Doctor had duels with Arabs. Ian won his fight and a knight killed the Doctor's assailant. (TV: The Crusade)
In 1866, Jamie McCrimmon and Arthur Terrall fought in the trophy room of Waterfield's house to challenge the location of the captive Victoria Waterfield. (TV: The Evil of the Daleks)
In Auderly House, the Third Doctor and Ace fought each other with swords. He disarmed her, but she grabbed his sword (actually a segment of the Key to Time and vanished. (COMIC: Time & Time Again)
On Fortress Island, the Third Doctor and the Master fought each other with swords. The Master lost. He threw a knife at the Doctor's back; it missed. (TV: The Sea Devils)
While posing as a robotic knight, the Third Doctor engaged in a sword fight first with Irongron, and later with both him and his second in command Bloodaxe. The Doctor came out on top, but his true identity was soon realised. (TV: The Time Warrior)
The Fourth Doctor joined in a swordfight in San Martino in 1492 to defend Giuliano against Count Federico's guards. The guards retreated after the Brotherhood of Demnos helped fight them off. (TV: The Masque of Mandragora)
The Fourth Doctor duelled with Count Grendel of Gracht on Tara. He emerged the victor, but the Count escaped by diving off the battlements of Castle Gracht into the castle's moat. (TV: The Androids of Tara)
The Fifth Doctor and the Tremas Master had a swordfight on 13th century Earth, albeit while the Master's identity was concealed. (TV: The King's Demons)
The Eighth Doctor battled the Master inside the Omniversal Spectrum - with both using swords and sheilds as well as their souls. (COMIC: Church of the Glorious Dead)
The Tenth Doctor and Fadros Pallujikaa had a sword duel which Fadros Pallujikaa lost. (TV: The Christmas Invasion)
The Doctor and Thane had a swordfight. (COMIC: Universal Monsters)
The Tenth Doctor tried to hold off a duo of Cyberman with a cutlass. (TV: The Next Doctor)
During the Battle of Demons Run, when facing the headless monks, Rory Williams, Vastra and Jenny fought with swords. (TV: A Good Man Goes to War)
Robin Hood challenged the Twelfth Doctor to a swordfight, but the latter elected to use a spoon instead. (TV: Robot of Sherwood)