re: Who is currently the best swordsman in Game of Thrones?

Jaime was a significantly superior fighter to Ned. Jaime at the beginning of the series was among the best 3 or 4 knights in Westeros. I was talking about this with a friend recently and here is what we came up with. We limited this to Westeros swordsmen, so Strong Belwas and the Dothraki aren't ranked.

Arthur Dayne - Jaime and Barristan (both highly skilled knights) praise his skill a ton. He can singlehandedly take down multiple trained opponents at one time. Possible GOAT swordsman.

Ser Gregor Clegane - probably not the most finesse in the world, but he sheer size and strength likely puts him above nearly anyone else in single combat. We don't know if or how much his "resurrection" has impacted his ability.

Ser Jaime Lannister - One of the most highly regarded Knights in the realm pre hand loss. He has won the melee a multiple tournaments and generally intimidates people.

Ser Barristen Selmy - A huge badass. Once went Middle Ages commando and snuck into a city to rescue Aerys by himself. Age has probably become a bit of a factor by the start of the show.

Robert - Young Robert was a complete badass who basically lived to fight and frick.

Rhaegar - Won multiple tournaments. Had an epic fight with Robert but lost.

Then there's kinda a significantly tier of really good knights that is hard to sort out - Sandor Clegane, Brienne (who is hard to rank because the show portrays her as more skilled than the books), Oberyn, Brynden Blackfish (age is an issue at this point), Loras Tyrell and probably more.