It's got to be the Varrock cleaner, only just winning (?) over the Varrock stray dog as the most useless NPC in the game.
According to the RS Wiki, the cleaner's job is to "help cope with the large number of ashes that often littered the streets of Varrock".
Really? Because all I ever see this guy doing is leaning on his broom around the east bank. The only times I've seen him sweep up ashes were when someone was trying to collect them for herblore. He rather enjoys pushing his broom around the Varrock east bank. I suppose he's cleaning up all that dirt and dust we adventurers track inside (read that with heavy sarcasm).
If he's really looking to do his job of ash removal, he might want to move his cabbage across town to the west bank and the GE, you know, where people are actually lighting fires.