Of course everyone has their own favorites. But let us begin with the pair who are on my icon: Hiro Nakamura and Ando Masahashi.
The first thing anyone notices about Hiro Nakamura is that he is so cute that it should be illegal. The second thing is that he is an enormous geek. Alone of all the characters, he specifically sought out his power (he bends time and space) and consciously adheres to a superhero code of conduct. His immense imagination, and the enthusiasm and zest for life that cause him, at the slightest provocation, to beam and run around shouting "Yatta!" and similar exclamations until you start to think somebody's going to slap him for being so happy, were badly suited to his previous life as an office drone.
Ando Masahashi, on the other hand, seemed perfectly all right in that life. Like many of the characters, he was very reluctant to accept the whole "powers" thing, and he hasn't got any himself, but by now he's seen enough to put his skepticism aside and become Hiro's faithful travelling companion and common sense on legs (unless gambling or a woman he's crushing on are concerned, when he can turn a bit stupid). Initially he also served as a translator, but what with one thing and another Hiro's English has improved quite a bit since then.
Like any good team, Hiro and Ando make up each other's deficiencies; Hiro with his head in the clouds (and very few useful day-to-day skills), Ando with his feet on the ground (and acute awareness that life is not a comic book and he could get utterly killed by hanging out with this guy). Certainly they are one of the most functional relationships on the show. They have bickered and even broken up, but they always come back together and forgive each other, because that's what friends do.
Of course, none of this could possibly get across the cuteness and good humor of their relationship as well as their own (subtitled Japanese) words. And pictures.
Hiro: I have discovered powers beyond any mere mortal.
Ando: Right. You and Spock.
Hiro: Yes. Like Spock. Exactly.
[a supervisor actually physically grabs Hiro by the scruff of his neck and drags him back to his cubicle]
Ando: Oi, Spock! Use the death grip, Spock! The death grip!
Hiro: A hero doesn't run away from his destiny. My only concern is whether I need to hide my true identity. Perhaps a costume?
Ando: You even mention tights and a cape, I'm going home.
Ando: Did you call the comic book writer?
Hiro: I left messages in Japanese. I need to learn to say "You're going to die in five weeks then New York will explode" in English. [looks at a phrasebook]
Ando: [in English] You are going to die in five weeks then New York will explode. [in Japanese] I'll teach you to say it phonetically.
Ando: Who is it (on the phone)?
Ando: I wish Destiny would lose our number.
Times to Follow..., by shay_renoylds
A few missing scenes about the beginning of Hiro and Ando's journeys. Hints quite skillfully at details of Hiro's background that have since been made canon.