Initially, I wouldn't watch anything that wasn't dubbed English.  Deathnote was the first series I watched entirely subbed, and now I much prefer it that way.

It just makes more sense, too; the show was written in Japanese, and therefore meant to be expressed in that language.  The whole perception of a character changes when the voice changes, and the difference between the dubbed and original voices is sometimes so great that it loses the original intention of that character.

Before I start a new series, I always ask fans which version is better.  If I don't get a conclusive answer from that, the deciding factor is whether the anime has focus on visuals or story.  I want story to be conveyed as originally intended as much as possible, but if I'm watching something visual like Cowboy Bebop, I don't want to be distracted by subtitles.

Now that I'm starting to learn a bit of the Japanese language, watching subbed but trying to ignore the text is good practice.