My family has had Tivo for about four years now, and absolutely love it. Enough that we've had a second unit for about the last year, on a second TV. With us needing all hands on deck each night around 7pm-9pm getting kids put to bed, it's great to be able to watch the shows we want when we want, rather than being tied to the networks' schedules.
We also really like some of the added features which are proprietary to Tivo only, and not to other DVRs. (Or at least that's my understanding.) Things like being able to view digital photos from our hard drive on the TV, access to Pandora (including use of our Pandora stations which were created elsewhere), Netflix access, Rhapsody access, Amazon movie/TV rental access, etc.
It's especially been useful for the past two months, as it allows us to skip all those @#$%ing political ads.
Note that we've never had any other DVR, so I really can't answer any questions comparing Tivo to anyone else. Also, we don't have cable, so any questions in that regard will need to go elsewhere too. But otherwise, if you have any questions about them, let me know, I'd be glad to take an attempt at answering...