It depends on the company doing the dubbing...
Until very recently, there has been this persistance in the states that "anime is a cartoon", and the tendancy is to not take it very seriously at all. I've sometimes been given the impression that some of the VAs they use are people they found by looking out of the window at casting time, and saying: "See that person at the bus stop? Ask them if they want this part."
In Japan, however, voice acting is considered a very serious and respectable career, and anime is a huge part of the culture; there are long running soap operas on a par with our own Coronation Street or East Enders that are entirerly animated

Therefore it's no surprise that a far creator attempt to produce a well acted film is made.
A lot of imported anime dubbings have been...questionable at best.
However, the trend is changing

With the market growing, most companies are starting to realise how much money is to be made from anime, and are making more of an attempt to dub it well. Recent releases like Full Metal Panic, Excell Saga (although obviously, it's hammed up beyond belief because of it's genre), Noir, Najika Blitz Tactics...as well as old classics like Trigun, Burnup Excess, and Tenchi (although granted, most of the supporting cast in Tenchi...with the exception of Kagato...were absolute Turkeys) and others have actually had some very good voice actors all round.
Overall, I prefer seeing things in dub for the most part...the only situations which I can remember finding the dub so unbearably aweful that I had to watch the Japanese version were the two most recently released DBZ movies (man did they butcher Brolly with that horrible dub...) and Azumanga Dio (absolutely amazing series...just...the dub kills it stone dead).
Since we're on the subject, here's bad dubbing at its worst...
In JapanesePicollo: ....You're a monster...
Brolly (with saddistic grin): ...Monster?...heh....No...I'm the devil.
In English 
Picollo: (can't recall the exact line...something like: "What an animal...")
Brolly: Of course...what do you expect...from a true freak!
...what the hell is that!?