Game of Thrones Warriors

I have seen many of Game of Thrones fans who desperately and childishly compare the characters of Game of Thrones to know who will win if X and Y have a fight. This grew with every one-on-one fights.

1. Ned Stark vs. Jaime Lannister (Season 1)
2. The Hound vs. The Mountain (Season 1)
3. Jaime Lannister vs. Brienne of Tarth (Season 3)
4. Prince Oberyn vs. The Mountain (Season 4)
5. Brienne vs. The Hound (Season 4)

The winner in each of these fights can not be determined due to circumstances and fitness level.

1. Ned Stark vs. Jaime Lannister - Ned Stark had become old and fat, certainly not at his best
2. The Hound vs. The Mountain - Hound was protecting Loras as well as he was aware of presence of the king
3. Jaime Lannister vs. Brienne - Jaime was chained
4. Red Viper vs. The Mountain - Red Viper was emotional
5. Brienne vs. The Hound - Hound was biten by Biter, which began to fester due to Hound's fear of cauterizing with fire.

We fans can deduce the better of Red Viper vs The Mountain. Prince Oberyn was clearly better than Mountain. He was just too emotional to avenge his sister's death.

Let's list down all the good warriors, mentioned in the series, worth listing down

1. Ned Stark
2. Jaime Lannister
3. Khal Drogo
4. Robert Baratheon
5. Jorah Mormant
6. Sandor Clegane - The Hound
7. Gregor Clegane - The Mountain
8. Daario Naharis
9. Loras Tyrell
10. Jaqen H'ghar
11. Syrio Forel
12. Brienne
13. Oberyn Martell
14. Rhaegar Targerean
15. Arthur Dayne
16. Barristan Selmy
17. Brandon Stark - Ned's elder brother

Let's analyse now.

Rhaegar Targerean defeated Arthor Dayne (competitive), Barristan Selmy and Brandon Stark in Tourney of Harranhal. 
Barristan Selmy considers Arthor Dayne over himself. 
Ned Stark was certainly not better than his brother, as the best of the house participated in Tourney.
Ned Stark defeated Arthor Dayne outnumbering him 7 to 3, so that doesn't count.
Ned Stark mentioned Arthor Dayne would have killed him if not for Howland Reed.
Robert Baratheon killed Rhaegar Targarean (2 cousins fighting over Lyanna Stark).

That makes

1. Robert Baratheon
2. Rhaegar Targarean
3. Arthor Dayne
4. Brandon Stark/Barriston Selmy
5. Ned Stark

Jaime Lannister mentions to Brienne that there are only 3 warriors who have chances to defeat him. Those 3 were The Mountain, Barriston Selmy, Loras Tyrell (or The Hound). 
Jaime also mentions before Red Viper vs The Mountain that if he had both of his hand, he might have had chances to kill Mountain. 
That makes Mountain over Jaime.
Hound and Mountain are alike in combats, probably Mountain is superior.
Brienne defeated Jaime and Hound both in one-on-one combat, under circumstances. But the two combats at least makes Brienne equal.
Brienne defeated Loras Tyrell fair and square without any circumstance advantage.
Red Viper would have defeated The Mountain.

Jaime and Ned Stark had a fight without result.
Hound and Mountain was also without result.

That makes

1. Oberyn Martell/Barristan Selmy
2. The Mountain/Barriston Selmy
3. The Hound/Jaime Lannister/Brienne
4. Ned Stark
5. Loras Tyrell

Khal Drogo, Jorah Mormont, Daario Naharis, Jaqen H'ghar and Syrio Forel have been in many fights, but not with the warriors we are ranking.
Khal Drogo can be named superior as he never lost, he was too strong and too agile for his size as well.
Rest are not known to be great fighters, though we haven't seen them lose. So lets keep them last.

Here goes my final ranking, though I am no expert.

1. Robert Baratheon/Khal Drogo
2. Rhaegar Targarean
3. Arthur Dayne
4. Barristan Selmy/Brandon Stark
5. Oberyn Martell
6. The Mountain
7. The Hound/Jaime Lannister/Brienne
8. Ned Stark
9. Jorah Mormont
10. Loras Tyrell
11. Daario Naharis/Syrio Forel/Jaqen H'ghar