Favorite sword can be an individual weapon, like Excalibur, or a type of sword, such as a katana.
My personal favorite is the preferred weapon of Sasaki Kojiro, a straight edge nodachi called the Dying Pole. The whole sword is weird and unique, and definitely sits in my No1 spot.
How about y’all?
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If we're talking type of sword- Katar, not really a sword though, more of a dagger... I appreciate the craftsmanship that went into old style folded steel Katana's. BUT If I had to pick a named sword as my favorite for legend and story; It would be Notung (aka Gram); placed during Signy's wedding party by Odin; and drawn from the great tree by her brother Siegmund; shattered by Odin before Siegmund can defeat King Lyngvi, and reforged by Sigurd the Son to avenge his fathers death, it's pretty much the inspiration for Elendil the sword of the King of Gondor and the name of the greatest and first King of the Dunedain men in Lord of the Rings