The new Tivo Stream is out and it's a pretty neat gadget, in my opinion. This device let's one stream or sideload TV to an iPad (or iPhone) using the Tivo app and will eventually be available for Android devices. I suspect that after the initial novelty of streaming, the Stream will be most used for sideloading shows for viewing while on the road.
The Stream works only on your local network but I know many are hard at work trying to make it work in the wild by using VPN. So far though, I'm not aware of any success with that. I'm not sure how practical it would be to stream through one's phone network due to the required bandwidth anyway. It would certainly not be practical if you have a limited data plan. The Slingbox (and Vulkano) hardware remain the only popular devices for streaming to the outside world and they, unlike the Stream, are able to adjust video quality on-the-fly to mitigate throttled bandwidth.
The Stream works only with the Premiere Tivo models although it will allow one to stream a show recorded on a TivoHD (on the same network, of course) by manually beginning a transfer to a Premiere and then streaming from the Premiere while the show transfers. And the Stream is capable of four concurrent streams if your network can handle that.
Protected content, such as premium cable channels, can be streamed but cannot be sideloaded for later viewing. In those markets where cable franchises enable the CCI flag on all channels except the locals, the Stream's usefullness is severly limited.
There are similar apps for streaming available from some cable companies (and the HBO app) but, as I understand it, not all channels are available to be streamed.