Should anime adaptations of manga stay faithful?

What's the one thing you always hear people say when they go to see a movie adaptation of a book?  Almost always, you'll hear comments about the book being better.  Taking a novel and cramming it into a 2 hour movie means that there are going to cuts along the way.  All the content isn't going to be there, and some things will have to be changed.  The end result is usually something that fans of the book don't really appreciate.  The same exact issues come up with anime and manga.

At least the translation from manga to anime isn't as rough.  With an anime TV series based on a manga, you have a lot more room to adapt the manga content.  You're not tied to a 2 hour movie that you need to cram full of content.  You have a certain number of half-hour episodes that can be used to explain a manga as thoroughly as possible.  Still, even with a much larger amount of time to work with, it doesn't mean that ever single manga element is going to make the translation.

There will be budget and time constraints no matter what.  There will also be content in the manga that just won't translate well to an animated feature.  The crew involved with putting together the anime adaptation will have to look at the source material long and hard to figure out what they can do to best preserve it. That is, if they don't feel like changing things up completely.

Indeed there are manga to anime adaptations that change things up completely.  Characters get added, storylines are changed, and sometimes all that's left of the manga is the name and a main character.  This could have something to do with the manga creator, as they're looking for an anime to take the license and run with it in a direction that works for TV.  You never know what the behind-the-scenes discussions really are.  We only get to see the end result.

When a manga does get an anime adaptation, what do you prefer?  Do you want to see the anime team take liberties with their interpretation, or do you want them to stay as close as possible to the manga?