Here's a good one. Only five housemates have ever made it to the final day without ever facing a public vote on their way to getting there: Brian, Dean, Ziggy, Mikey and Josie. Elizabeth made it to the final week without ever facing a public vote, but was eliminated early. Kinga made the final, but was only in the house for one other public vote, from which she was immune by means of passing a task. She did however beat Craig into 4th place.
Additionally, several other housemates have made the final without being put up for eviction by the result of nominations.
Shell faced eviction twice, but by means of tasks and twists.
Anthony only faced eviction in an all up week.
Pete was only nominated in the best-friends week, and in the all-up bar Jayne week
Glyn was up for eviction twice, but only by not making the Brotherhood, and in the all-up bar Jayne week.
Samanda only faced eviction as a penalty for agreeing to become one housemate
Brian and Liam were only up for eviction for not becoming "gurus"
Kathreya was only up for eviction as a punishment in the week most of the house went up
Sophie, Rodrigo and Charlie faced multiple evictions, but they were all either punishments or all-up weeks.
Andrew was only nominated as the result of a Save/Replace task. He also was involved in an all-up week.
Also:
Stuart made the final week having survived two evictions, by means of tasks and twists.
Craig faced eviction twice, but was put up by the Makosi twist in Week 1, and in an all up vote in Week 2.