There are two things I look for when watching an anime based on the plot, the progression or the climax. On a second run, I already know what will happen in the story so there's no surprise like when something totally unexpected happened the first watch. It's possible to enjoy walking the path a second time, but when it comes to the end of the path, I already know what to expect making the ending seem less meaningful.
The obvious exception when rewatching a story is when a manga or light novel is adapted into an anime, but the advantages of watching anime outweigh the fact that it's the same story. Colour, animation, voice actors and hopefully good directing all make it worth watching the same story twice.
Other than my favourites and classics I haven't seen for many years, an anime based on plot isn't the best idea to rewatch. This is where recap episodes can come in handy to save time by watching just a few episodes to summarise it. My favourite anime, Bungaku Shoujo, is short so it doesn't need recap episodes, 4 OVA episodes and a movie won't take long to complete. It might be based on plot, but as my favourite, it's well worth watching again.
A gag manga or 4-koma is a good choice to rewatch because I'm not missing out on the original expectations. Comedies don't really have a plot so I can just sit back and enjoy. K-on is a good choice because there are five girls basically doing nothing, but still makes it seem like something. It is one of the best ways to waste your time.
So how likely are you to rewatch an anime series, or is the series ruined because you already know how the story will progress?