Most non-TiVo DVR's (DishNetwork, and Cable Company Brands) are just digital VCR's with the added functionality of controlling live TV.

Here are my main points with TiVo that justify the cost of 3 DVD rentals a month.  It's normally $12/month but with DirecTV it's only $5 unless you've got the high-end package then it's included.

1.  TiVo doesn't rely on a time to record a show.  It relies on the show name and station.  So if there is a special episode of Survivor on Tuesday instead of at its regular Thursday slot...TiVo will record it and you didn't even know it was on until you sat down.  You don't have to remember when something is "on" since TiVo takes care of it.  You worry about when you can watch it. :-)

2.  To go along with the non-time dependant theme:  I love Seinfeld and always want two episodes available for me to watch.  I search for Seinfeld in the show listings and it shows me the different networks that have it.  I pick the network (Fox for me) and it will record them and keep two episodes available for me.  When it's time for the 3rd episode to record it will automatically delete the older of the previous and record the new one.  It will also not re-record any episode that's been recorded within the past 28 days...so it keeps two fresh shows for me.  There's still a lot of customization there also.  Example for new shows, I can tell it to only record new episodes (say The Amazing Race) because it's a new season I don't want to see any reruns.

3.  If you've got kids (I've got 4 under the age of 7) - you can always have a few of their favorite shows on so they're there when you let them watch TV - also lets you keep track of what kind of stuff your kids are watching.  It also has a parental controls that won't let it record or view shows based on the rating limits you set without entering a secret code.

4.  If you are into shows or movies based on the type of movie it is or you have favorite actors/directors.  There is an item called a wishlist that's like google for TV.  Enter in some keywords, specify if they should show up in the title or in the title and description and that's it.  If a show/movie comes on that matches that criteria it will record it for you..no matter what time it comes on.  There's lots of customizations on that too - down to show categories (drama/action) and show types (reality/game show/sitcom) those are just examples since the lists are very extensive.  Example:  I like John Cusack and when I was younger there was a movie on HBO called "Hot Pursuit".  I entered that as a title wishlist and 3 months later it showed up in my now playing list.  It came on TBS or something late at night and TiVo got it for me.

5.  Let's say you're watching a show/movie and you see a commercial for something that's coming on another day/time.  Stop you current show and go into TiVo and tell it to record that show for you.  Now, you don't have to remember to be in front of the TV and later, when you have time, it will be there for you to watch...and if it stinks you've not wasted your time - you just delete it.  That happens to me a lot with shows on the History channel.

6.  Let's say you happen to be watching live TV and you run across a show/movie that's on and already started.  You can click a few buttons and TiVo will tell you the next time that it's coming on and you and have it record it for you.

All of this comes down to getting your money's worth out of your cable/sat bill and your time.  I no longer watch TV based on the network's time schedule - I watch it on my schedule.  When I'm have time and I'm ready to watch some TV I know there will be something on that I want to watch.

Here is a link to a good community for TiVo'ers.