Joel Waldfogel of the Wharton School at the University of Pennsylvania has published a study of students at his university on this. Here is his abstract:
In the past few years, YouTube and other sites for sharing video files over the Internet have vaulted from obscurity to places of centrality in the media landscape. The files available at YouTube include a mix of user-generated video and clips from network television shows. Networks fear that availability of their clips on YouTube will depress television viewing. But unauthorized clips are also free advertising for television shows. As YouTube has grown quickly, major networks have responded by making their content available at their own sites. This paper examines the effects of authorized and unauthorized web distribution on television viewing between 2005 and 2007 using a survey of Penn students on their tendencies to watch television series on television as well as on the web. The results provide a glimpse of the way young, Internet-connected people use YouTube and related sites. While I find some evidence of substitution of web viewing for conventional television viewing, time spent viewing programming on the web – 4 hours per week – far exceeds the reduction in weekly traditional television viewing of about 25 minutes. Overall time spent on network-controlled viewing (television plus network websites) increased by 1.5 hours per week.
Updated 11 November 2007:
For another view, see Richard Wray's, Young networkers turn off TV and long on to the web:
... The EIAA study shows the effect on TV viewing, especially among the youth audience which is using the internet more often than TV for the first time. The survey shows that 82% of 16- to 24-year-olds use the web between five and seven days a week while only 77% watch TV as regularly - a drop of 5% from last year. ...
Link: The Guardian. --Dennis