There are two types of video quality - standard definition (SD) and high definition (HD). Please make sure that the Service Plan you are subscribed to supports the video quality you are trying to watch. NOTE: For streaming, you are interested in the "sustained download" speed.

Video Quality:
Standard Definition (SD) - 480 dpi
High Definition (HD) - 720 dpi and higher

Amazon Prime Instant Video:
Standard Definition (SD) videos: 0.9 Mbps
High Definition (HD) videos: 3.5 Mbps

Netflix:
1.5 Mbps - Minimum for for SD quality
3.0 Mbps - Recommended for SD quality
3.5 Mbps - Minimum for for HD quality (720 dpi)
5.0 Mbps - Recommended for HD quality (1080 dpi)
25 Mbps - Recommended for Ultra HD quality

Hulu (Plus):
720p - a minimum of 3.5 Mbps downstream bandwidth is recommended. 
480p - a minimum of 1.5 Mbps downstream bandwidth is recommended. 
360p - a minimum of 1.0 Mbps downstream bandwidth is recommended.

Vudu:
HD - 2.25 Mbps or higher.
HDX - 4.5 Mbps or higher.

Skype
For simple video calling, 300 kbps (kilobits per second) is largely sufficient. For HD video, you need at least 1 Mbps.

Apple Facetime
Sending HD video requires a minimum upload bandwidth of 1 Mbps.
Receiving HD video requires a minimum download bandwidth of 1 Mbps.

Online Gaming
XBox Live, PlayStation
SD video streaming - download speed of 1 Mbps, upload speed of 0.5 Mbps.
HD video streaming - download speed of 3 Mbps, upload speed of 0.5 Mbps.