Depends a lot on the individual shows. If an anime deals with a lot of japan-specific humour or japanese culture I'll never watch it dubbed because it just removes some of the cultural nuances for me. On the other hand, shows like Black Lagoon, Michiko to Hatchin and Ghost in the Shell are vastly improved by the dub. English just enhances the grittyness since it's better at expressing more negative attitudes, I feel. Prime example is Revy from Black Lagoon, who's an uncouth punk in the sub, but a coarse, curse-spitting bitch in the dub. And I love it. As should anyone else.
On the flipside english VA rarely do a good job with moe stuff. The dubs usually just end up shrill and annoying, rather than sweet and bubbly. Definitely gonna go with subs on the rare occasions where I do feel like watching some moe fluff.
Lastly you've got the dubs where the translators just butcher the script to fit in dumb pop culture references or political jabs. These you should always shun. Thus is my command.
Discuss individual shows here