I have a Hauppauge WinTV card. It works very well and I would recommend it to anyone. As I understand it, in the early days of TV cards, the quality was poor, and there was a serious CPU hit. Fortunately, PC technology continues to improve at an almost frightening pace. My card has the following features:
The teletext support is terrific -you can click on a page number on the screen and it loads that page, like some kind of 1980s version of the world wide web. You can also write scripts to load a particular set of teletext pages for you to read at your leisure, save teletext pages, set your computer clock to the teletext clock; indeed, almost anything you could want from teletext software is implemented. On the other hand, you can't get away from the fact that it's, well, teletext.
For the remote control, you get a small button-sized sensor on a wire that plugs in to the card. I Blu-Tacked the sensor to my monitor, but you could put it wherever was convenient.
The full product range also includes cheaper cards that don't support stereo or teletext, and more expensive cards that provide radio support.
I bought my card when I was a student living in limited space - the computer monitor was already taking up space, so the TV card gave me a TV without taking up any more space. This was the main advantage over a normal televsion, although it was also significantly cheaper than a television with equivalent specification.
Sitting at a normal TV-watching distance, it looks just like a television. Sitting up close, with it in full-screen mode, it doesn't look perfect. However, this is because a high-resolution computer monitor is ridiculously over-qualified to display the relatively low resolution television signal - it's not so much a fault of the technology so much as an inherent flaw of the medium.
I've had no problems with mine at all. The card does everything you could possibly expect from it, and does it well. I should point out that this was under Windows; I believe Linux support is patchier. Update 2004-02-20: I now have the card working just fine under Linux in a MythTV box and it required almost no effort to get it working - just had to load the correct kernel module and away it went. I haven't tried the teletext though.
As a side note, an interesting side-effect of the card is that it eliminates overscan. On a normal television, a certain amount of the transmitted picture is lost, because the crude (compared to a PC) hardware maps the picture 'over the edge' of the visible screen a little. Watching TV on my TV card, I notice that all the (ghastly) station IDs look a few centimetres 'further in', because the digital card wrings every possible pixel out of the signal, thus displaying the 'whole picture' on screen.