I like posted "parts" to be a complete scene, at least, with it's own little self-contained plot. I personally find it very aggravating when the villian has kidnaped his victim, and has just ripped her clothes off, and... "to be continued".

This is really a problem on story boards that are "forum" based - each part is posted to a discussion forum. It is sometimes very obvious that the author is typing his/her story into the "message" box on a form, and is submitting each little snippet as it is written. On big problem with that approach is purely practical - it pushes other people's stories off the front page when it takes you 3-4 posts to complete a single scene.

My own approach is to write long stories in a journal format - "here's what happened today". I'll make each chapter a self-contained short story. Each chapter clearly follows the previous one, as far as character development and overall plot goes, but I try to write so that a reader can sit down and read a single chapter and feel like they've read a complete story. Each chapter will basically represent a single day or single event in the life of the main character(s). The space between each chapter is usually undefined; the vignettes are simply in chronological order. This is especially true in my spanking stories - my characters are not going to get a severe spanking every single day, so there's no need to have each chapter lead smoothly into the next. Rather, Chapter 1 can describe the events leading up to a spanking, and finish with the spanking that has been earned. Then Chapter 2 does the same thing - different events, different misbehavior, but again leading up to a spanking - maybe more severe than the first, due to "behavior getting worse".

Because I usually have several stories "in progress", I don't want to leave readers waiting to find out what happened. And my methods allow me to post a part of this story, then a part of that story, then maybe a standalone short story. Keeps me from getting bored.