Tivo has an iOS app. It allows you to do exactly what you want. Control the Tivo, browse TV listings, etc. It sucks to use as a remote as you have to look at it to make sure you're hitting the right button. It's also slower, as you can't just slide your finger around on the screen to get to the next button. With a regular remote, you usually quickly learn your way around it by feel and can use the common buttons easily without looking.
The listings don't work well on an iPhone - the screen is just too small. The guide on the TV screen works much better. It's easier to read and you can fit a lot more information on screen at once.
I haven't tried it on an iPad yet. I'm guessing the listings would be better, but the remote controls would probably be even slower to use with the larger screen.