Do I have to use my cable co's DVR box 4 service?

Sorry if this isn't the proper posting area, i'm not sure what forum it should be under besides that it's using digital tv service so....

I just wanted to know if I can buy a non-subscription DVR box to use through my cable provider, instead of using their box that I have to pay to use for service and rent. I'd rather buy one that doesn't need subscriptions, (like TiVo) does something like this exist or are they all subscription based?

If I can buy my own from someplace, can I just hook it up to a cable box and i'm up and running, or is the signal actually blocked from the cable company unless I pay for DVR service to be enabled? I'm a newb at this so if the questions seem dumb, please don't hammer on me. I've been trying to find info on this topic and most links are always about the home security dvr systems.
Thanks anyway!