Sennheiser, AKG, Grado (not sure if they make noise cancelling), audio technica as mentioned, all good options. Bose are no better than those 'Beats' headphones that Monster Cable is trying to peddle. That isn't to say that they are bad headphones, just bad for the price.
The way I see it you have two options. First option is to get your set re-cabled. Either your left or your right connection is broken somewhere. Try your local audio shop (think stage, lighting, not musicians), or a car audio place even. I can't see it taking more than an hour to have new cable done. Your second option is to go to Head-Fi.org and start doing some research into your next set of headphones. Keep in mind that some enthusiasts have their headphones re-cabled regardless, so consider the cost of that if you do decide to go with a different set of headphones.