My experiences tell me that base stat-weak Pokémon typically don't last long in Nuzlocke runs. This is to be expected- if they're not powerful, it becomes difficult to keep them alive at high levels. However, in my Yellow run, I captured a Rattata. I named him Major, and in the comic script that may or may not be finished one day, he kind of had the personality of a grizzled war veteran. He was captured on Route 3, and didn't level as fast as either my Pikachu or Spearow. I kept him around, though, because more manpower is always a good thing in these games.
I encountered the Team Rocket trio at the end of Mt. Moon, and they proceeded to lay a total smackdown on my team. THey killed my Pikachu and Spearow, leaving me with only Major. Thanks to a streak of lucky criticals and low enemy accuracy, he managed to survive.
I built up the team some more, and eventually arrived at Giovanni's gym. My team consisted of Major, a Venusaur, and four others that weren't likely to be one-or-two shotted by Ground-type attacks. I led with Venusaur, who had been powerleveled to 60. His Dugtrio's first attack hit. That hit happened to be Fissure. I watched my team drop one by one, inflicting minimal casualties... Until Major came onto the field. I had given him Blizzard a few levels back just to clear up inventory space. He proceeded to sweep the remainder of Giovanni's team, once again the sole survivor of a massacre.
Sadly, his luck didn't last forever. I used him fairly regularly during the Elite Four, but kept from using Blizzard. I fought Lance, and managed to get him down to just his Dragonite. It somehow survived a critical hit from Blizzard, and retaliated with its own Blizzard. Major didn't survive the hit, but he did lower Dragonite's HP enough that my Flareon could KO it.
I ended up winning that league challenge, and I get the sense that Major was the biggest part of it. If the comic ever finishes, his last words are going to be ones of support. Words of hope for the one, final, personal battle that awaits...