With digital technology it has gotten almost impossible to figure out where right ends and wrong begins. I think it is largely a personal choice about what you feel is right. I have hassled my friends over pirating things before, but I would not even consider hassling you for downloading a show that you bought the $200 box set for. That being said, you will find fewer cases of moral ambiguity if you just keep it simple and only use what you bought--if you just said 'well, I'd like to watch this show but I forgot to bring it and I didn't take a copy from the discs I bought, so I guess I'll have to wait' you would be in 100% okay territory. It is a question of whether you can deal with the inconvenience of waiting a short time before watching your show.
A lot of people make excuses about piracy, and some of them are pretty clever--the vinyl argument someone used earlier, the 'I have this on vinyl but I want to put it on my iPod,' is one I'd never heard before!--but it really just boils down to a question of ease. It is really easy to pirate something, and there are virtually no consequences for doing so. Dress it up however you like, but this is the reason most people pirate: because they can get away with it.
Most of the justifications really don't hold up. For instance, take the vinyl argument: you bought that particular record, and that particular format. I'm not sure if this is old vinyl, or if you got it as some sort of collector's item, but the process of creating a record is very different than creating a digital version, and you only bought the record version. You did not buy that song, for all eternity and in all forms. If I buy a 30 year old cassette tape for $.25 at a garage sale, do I have the right to download for free every song on that tape, even though they're now selling for $1 a piece?
Imagine if we discovered a new way to make computers (say they're optronic rather than electronic) that is far superior but requires everything to be remade and reprogrammed. We all own operating systems now, and tons of software. Do we have a right to expect all that stuff for free on our new optronic computers? Keep in mind that people had to spend money to program and develop that software. In order to offer us those products, the companies spent time and money. If nobody pays them for their time and money spent, they will go bankrupt. And why would somebody spend hours and hours doing hardcore programming for free? If that's the case, they would probably program something that was enjoyable to them personally, rather than useful to society, and that would be a loss for everyone.
Now, I definitely understand the indignation a lot of people have towards software companies. They are, with very few exceptions, jerks. They claim that piracy is a much bigger problem than it actually is, bully their legitimate customers trying to combat piracy, release version after version of essentially the same product, but slightly altered to wring more money out of their customers, release deliberately incomplete versions to squeeze out more money, try to deny people the use of the ease of digital reproduction, etc. There are plenty of companies and products that probably do have it coming. But my feeling is that if you are going to use something, you should compensate the people who created it and made it available to you, because it sucks doing a lot of work and getting little or nothing in return for it. You would be mad if you spent tons of hours researching something for your boss, only to have him tell you, after you finished it, that he went onto Wikipedia and found what he needed, so your research report is unnecessary and you won't be paid for your work. So don't inflict that on other people.