We have the following networks:
1. telephone (fax)
2. television
3. internet
4. mobile phone
Telephone Company: ADSL is to use the telephone network for internet connection, and to go a step further, video on demand can be made to work with ADSL. In that sense, the telephone network is now to provide TV, internet as well.
Cable TV: Cable modem is to use the cable TV network for internet connection, and voice over IP can be made to put telephone services on the same network. In that sense, the cable TV network is now to provide TV, telephone and Internet.
Mobile Network: Recently, I've subscribed a service which is based on mobile phone network to provide internet access, as well as conventional telephone service. It's not very fast, but then I believe it's fast enough for most people. Of course, it can support video on demand as well.
Who will win finally in the war of network convergence? Personally, I think Internet will rule in the form of optical fibre services provider since it's fastest and thus it can provide all sorts of services nicely, and the second candidate should be the mobile phone network, since nothing else could replace it.