One thing that I like about subbed anime is that I can watch a wider variety of anime that hasnt been dubbed yet, or will ever be. This can give me some real Jems of animes, like when I watched Lucky Star before it was dubbed, and I still fell in love with the series. Also subs allow me to hear Japanese voice acting, which can sometimes be a welcome break from hearing English all the time. Also subs can provide an alternative, if the dub was FUBAR.
Well I have a hard time deciphering subtle emotions while listening to Japanese, and reading subtitles, which are often in some ridiculous font. Most subs are done by fans and it can be hard to trust them in translating it right, which can be hard when they misspell words in the subtitles. Also they have a tendency to not display the subs long enough to read and I find myself stopping and rewinding to re-read the subtitles. I usually have to do the same thing when They put in a note about japanese culture.
Overall I would have to say that if you gave me a good anime with a good dubbed version and a good subbed version, I would probably pick the dub, but subs do have there merits.