A cable card replaces a cable box (or dvr), so you'd only need one or the other. Some HDTVs have a slot built in for them, as do the TivoHD and Tivo Series 3. They allow the TV or Tivo to view digital and HD channels without needing a box (think back 20 years or so when they called TVs "cable ready").
There are single stream cards (which you would use if you put it into a TV) and multi-stream cards (that allow a Tivo's dual tuner to function). A cable card only works "one way", though, so it doens't allow you to access PPV or OnDemand.
A cable company will give you a card for free instead of a box when you sign up for digital service. If you want digital on two TVs, a card only costs about half per month what an additional box would, so you could save some money there by having one free box and then paying the monthly rate for the card.
The problem with them is their reliability. I've read countless horror stories from other Tivo owners about how the installers don't know how to install them properly, how it takes an hour to set them up, and how they'll often lose channels or need to be re-activated. Tivo even suggests that you ask the cable company to bring a few extra cards because so many are "bad" when they're installed. Because it takes so long for them to activate, the installer often leaves during setup and the customer doesn't realize they've gotten a bad card until its too late.
Personally, I like Tivo. I like that they exist and offer an alternative to throwing more money at the cable companies. I like how easy it is to use and I like the extras they provide (download movies and music videos, transfer shows to laptop or ipod, expandable hard drive, wireless, etc). A few years ago I had Dish Network for about a week and absolutely hated their DVR. From others I've spoken with, they agree that if you've had Tivo its almost impossible to go back to a regular dvr. Although if a regular dvr is all you've had, you're usually happy with it.
The only reason I'd get a cable card for my Tivo is if I wanted to go to Digital Value and get the couple HD stations that aren't available with QAM (ESPN, CSN, Discovery, etc). Other than Sox games, though, there's not much on those stations that I'm really missing in HD. So for now, I'm not going the route of a cable card.