I don't always react well to movie adaptations (coughharrypottercough). However, I love what I'll call "alternate stories", things like modern day retellings, stories from minor characters points of view, things like that. Obviously, there are going to be differences, sometimes dramatic ones but I don't mind them as much in these cases.
I think the main difference is whether I go in expecting it to be dramatically different, or if I go in expecting it to be faithful.
For example, when I watch Once Upon a Time on TV, I expect the fairy tales to be different from what I know. In fact, I'd be disappointed if they didn't change the story. As long as there are familiar elements though, I'm happy. This is because (as I define it) Once Upon a Time is inspired by fairy tales. The Harry Potter movies on the other hand are based on the Harry Potter books and therefore should have a greater level of fidelity.
To be clear, I understand that when some thing is based on another work, changes will occur between mediums. These things I don't mind. As long as the information is given to the audience, the exact method may change.
For example, if The Hunger Games had been completely faithful to the book (and on the most part it was actually), most of the movie would be voice over, as the book is narrated by Katniss. While voice overs can be done effectively, the movie would be less interesting if most of it was Katniss walking and explaining something. However, there was still vital information that needed to be told to the audience. As an example, in the book Katniss explains what tracker jackers are when she encounters them. In the movie, Ceasar Flickman and Claudius Templesmith who are acting as commentators for the viewers at home, explain them as part of the commentary. This is a change that makes sense within the context of the medium, but still keeps the story the same.
I also don't really have a problem with movies condensing events, or removing characters that don't have much to do with the story. Examples of this would be Bill and Fleur's wedding happening on Harry's birthday in the movie, even though it's not the same day in the book. In Hunger Games, the character of Madge is removed and the story is only slightly affected.
What annoys me in adapations that at based on, rather than inspired by, is when important subplots are removed, especially when the filmmakers add in sequences that make no difference to the story in their stead (I'm looking at you Harry/Hermione dance scene but no mention of Tonks being pregnant except for a mention of son in the next movie!).
By the way, I've been focusing on book/movie adaptations, but I know there are other adaptions. I remember seeing Little Shop of Horrors get turned into a musical. That was weird. Also, movies get video game adaptations, though I views those as inspired by, rather than based on.
I just wanted to touch on this, mainly to work through my own hypocrisy of complaining about changes in some adaptations, but loving things like Grimm, Once Upon a Time, Sherlock and others. Also, I hope this makes up for yesterday's lame post.