When you rent a DVD from Blockbuster you have to take it back after a day or two, if not you have to pay again to keep it.
When you rent a car that has to go back, even if you rent it for 6 months, you can't just say "oh, i've had it for long enough, it's mine now" and stop paying.
Why do people think music is any different? If you want to rent it there has to be a method of stopping access to it if you stop paying.
I subscribe to Napster. It works on my PC which is connected to a stereo, it works on my phone and I can connect that to my car stereo. I've no problem paying them their 15quid a month and continuing to pay it to keep access to the music - they do add new stuff all the time.
If you want to keep the music/DVD/car then buy it outright - don't rent it in the first place.