I think the reason that Kirk and Spock work so well as a pair is that they're a classic example of literary foils. For those of you who need a brush up on English class,
"In any narrative, a foil is a character who contrasts with another character, typically, a character who contrasts with the protagonist, in order to better highlight or differentiate certain qualities of the protagonist."
The only reason why Spock is so interesting is that Kirk is so normal. Kirk is a classic 60s heroic protagonist. He follows his intuition, is a classic leader, and is super conventionally attractive. Spock is Kirk's uber-logical subordinate, who is a little funky-looking. He makes interesting and intelligent points that a regular human character wouldn't make. Even though he can come off as cold and emotionless, his relationship with Kirk humanizes him throughout the series. If you love Spock's weirdness and Kirk's normalness, you'll love these hilarious Star Trek memes.