If American boxed wine is all alcoholic Kool-Aid, as narzos describes, then there's a good reason why it's stigmatised - it's not wine. Happily, over here in the UK, wine-in-a-box is not merely the preserve of get-pissed-quick sorority girls.
Don't get me wrong - to turn up to a dinner party with a three-litre box of Stowell's Bulgarian Cabernet Sauvignon is still considered bad form, but a box of wine is both excellent for those who drink small amounts very frequently, those who are hosting a party and don't want to be opening bottles every five minutes, and those who drink entire boxes in one night. Alone. While watching entire series of Ally McBeal on video.
As for the quality of said wine, well you would be a fool if you picked a box over a bottle - simply because of the difference in taste. I would liken the difference in taste between bottled wine and boxed wine to the difference between a bottle of Coke and a can of Coke. Ostensibly the same thing, but slightly more metallic. However, the taste of wine from a box that was first drunk from a week ago is infinitely superior to the taste of wine from a bottle that was opened seven days earlier. Hence the beauty of wine in a box.
As a rough guide to the quality of wine you're getting, look at the price for the standard three litre box. Cheap plonk comes in at 10-12 GBP. If it was bottled, it'd likely retail at three quid. A box that weighs in at 14 or 15 pounds Sterling is equivalent to a £4 bottle of wine. And if you stretch to twenty crisp notes for your box, you'll be getting something very drinkable indeed - think something like a Corbett Canyon (California) or Hardy's Stamp (Australia).
In my experience, boxing is kinder to wines that are full-bodied and deep, such as a Cabernet Sauvignon or a Shiraz. The difference between the bottled and boxed varieties of any given wine of this type is minimal. However, fruity, softer wines such as Beaujolais or even some Riojas will suffer somewhat by their metal confinement.
In conclusion...Yay Wine-in-a-Box.