It really depends on the anime and the cast.
If it is the english dub for something like Baccano, Black Lagoon, GitS SAC, and Hellsing Ultimate then I will gladly watch it dubbed. Even if it isn't anywhere near as good as long as it sounds more than enough I am willing to give it a try.
Like the recent announcement for the Fate Zero dub with the 2 minute video of everyone only having 1 line in english. I mean the dub cast and their roles seem just mostly perfect. Crispin Freeman as Kirei SHUT UP AND TAKE MY MONEY and Jamieson Price as Rider just feels like perfect. Pretty much a lot of it seems perfect, I really can't wait for the dub to come out, and I do feel it could be one of the best dubs to come out.
http://www.youtube.com/watch?v=/rl94WZWya-M
There is also some anime where I like both the English dub and Japanese dub so much it is harder to pick which one of the 2 is my favorite. Most of the time I will ofc go with the sub being better even if only by a little bit.
Some anime that come to mind at the moment
Death Note - I have seen it multiple times with both dubs
Haruhi Suzumiya - The Japanese dub wins over me but I like Crispin Freeman as Kyon the same amount as I like Sugita voicing him. (Sugita is probably my favorite Japanese voice actor while Crispin Freeman is probably my favorite English voice actor.)
Fullmetal Alchemist Brotherhood - I like both versions equality its really hard to pick
I know a lot of you are English Dub haters but don't hate on all dubs especially if you have not watched something dubbed. Not all dubs are bad especially in most recent years where most dubs I have heard are from mediocre to really really good. Like one of the most recent English Dubs that I want to watch to is Steins;Gate because it sounds really good based on all the previews I have seen about it. Just keep a more open mind when going to watch something in English and make sure it has a pretty good dub before watching it in English.
But ofc most of my favorite anime are only out subbed because I like comedy a lot with Japanese references and parodies it is really hard to dub like Gintama which they dubbed the Movie and it turned.....not that good.
I could go on forever.....so yea tl;dr not all English dubs are as horrible as most anime fans make it out to be. If I was to recommend 1 anime for you to at least try to watch the dub I would say Cromartie High School is the one. https://www.youtube.com/watch?v=nrI7QUJfkvI lol