For me I like the majority of the factions, but Noxus really stands out to me, in particular the more "traditional side", with fellows such as:

I hope Draven and Urgot actually count here.
Noxus is a nation of strong men and women who became strong through persistence, dedication and unwavering will. While some are born to nothing and other are born with everything the truly strong are those who command the most respect. Even if you are a forgotten orphan you can rise up to claim what is rightfully yours, as long as you have the strength to carry a weapon and bury it in to the fools who would try to stop you.
The thing that really got me about Noxus was the dichotomy between it and Demacia, in many areas but particularly in war. Demacians are organized and conscripted; they are numerous but they're aren't bred for battle as Noxians are. Sion and Darius are prime examples; soldiers who turned the tide with action and will power, who did what hundreds of Demacians couldn't do. Noxus values the worth of individuals as long as you can prove yourself.
Like wise justice is in the hands of the strong in Noxus. If you have the will you can bring it down on any you see fit, and those people are just as free to do the same to you. Of course a civilized nation has laws in place there's no shame in killing someone. The act of actually killing is in itself a sign of strength; only the strong can truly commit such an act.
One other thing I really like is the conflict internally in Noxus between the Black Rose and the true Noxian way. The Black Rose is deceitful, traitorous and rely on magic to do what they do. They lack true Noxian strength, and the struggle between the dark shady side and the strong warring side of Noxus is really compelling to me. Which is why Swain's cool, because he exemplifies true Noxian strength but isn't afraid to rely on those old alliances with LeBlanc if the situation calls for it. He's in control of everything despite what some might believe.
Also another thing; I really love when humans are depicted as being insanely powerful in a physical sense despite being ordinary humans. As such Noxus is really cool to me because it has many examples of humans showing physical prowess that would be impossible for normal humans. Their soldiers aren't as numerous as Demacia's, but they're ten times stronger.