LOL!
I actually have a cousin who is co-founder of a company ("Biblica"? I think?) that promotes reading the bible entirely without the "versification" and "chapterizing" - both of which are great if you're doing a detailed study, but not so much if you just want to read the story.
I was delighted to discover that http://biblegateway.com provides a mode where the verse numbering disappears. When you combine that with a "printer" view, you can actually read a chapter of the bible at a time without those distractions!
I just got used to it and the numbers fade into the background. I'll check it out and see if I notice. I've been using http://biblehub.com/ i don't think it has this feature. it has many different versions. I'm most used to KJV and NIV, but have used many more. My parents raised me to be a minister. Sometimes it's like wearing scripture colored sunglasses.