Nurse: very useful to get pylons in most biomes because arms dealer + nurse = forest + desert + cavern + ocean + mushroom + jungle + hallow pylons. It's only the snow pylon you can't get this way. (And the universal pylon, of course.) Also required for the achievement about getting hurt a lot.
Dryad: purification powder, seeds, planters, also a useful combat buff.
Mechanic: grand design + actuators + timers = most useful NPC for cheesing the game.
Steampuker: clentaminator + teleporter + asphalt block + conveyor belts = best arena building NPC.
Stylist: vanity/cosmetics only. It's cool she provides special hairstyles after beating certain events, but who ever uses that?
Party Girl: bubble blocks are pretty useful. Balloon blocks can be good for building stuff due to the roundish shape they take.
Princess: NPC happiness booster, source of rare items in 5162011
worlds.
Zoologist: town pets, starter whip, starter mounts, Molecart, universal pylon.
Based purely on utility, Mechanic would be my first choice. Steampunker is a close second but you need Mechanic to use teleporters and logic gates anyway. Zoologist would be third, Dryad fourth, then Party Girl, Nurse, Princess, and Stylist in last place. Princess gets to go above Nurse and Party Girl in Celebration worlds.
But there is an additional contender: Lost Girl. The favorite NPC of everyone who is trying to build a cell phone, gimmie my metal detector!