Standard definition television   3.5 Mbps
DVD movie quality steaming   9.8Mbps
High-definition video television   10-15Mbps
Blu-ray video   Up to 40Mbps

 

However, in general, you should consider these sort of figures for watching videos online (as they will have been encoded/compressed/squashed):

DVD quality   3Mbps
HD quality   5Mbps
1080p quality   7Mbps
3D Films   12Mbps

 

However, in case you’re interested, the following are official guidelines from different broadcasters:
iPlayer

SD Video   2Mbps of sustained bandwidth
HD Video   3Mbps of sustained bandwidth

 

Netflix

SD Video   2Mbps
720p HD video   4Mbps
„The best video and audio experience“   5Mbps

Hulu

720p video   2Mbps
„The best quality HD video and audio“   3.2Mbps

 

Vudu

SD video    1.0-2.3Mbps
720p video    2.3-4.5Mbps
HDX 1080p video    4.5-9.0Mbps
3D HD video    More than 9Mbps

At least as important as the speed of your internet connection is the consistent speed of your home network.

If you will be connecting a device to the network with an ethernet cable, there will definitely be enough bandwidth. If you intend to use WiFi, and your modem/router is old and/or in a room far away from the device, you may find that is the limiting factor.

If you have a laptop, you could try placing it where the DroiX® device would go, and visiting http://www.speedtest.net/ – click the Begin Test button, and you should find out how fast your WiFi connection allows data to be transferred from the internet. If you plan to watch HD videos, consider either directly wiring your DroiX into your home network, or using network adapters that use the mains wiring in your house as a network cable.

Also, the figures quoted above assume that no-one else in your home is using the internet at the same time, and that other internet users in your area aren’t slowing down the whole neighbourhood.