It depends on who's uploading it. In many cases the companies with copyright ownership of old TV shows are uploading them to YouTube. For example, both Johnny Carson and David Letterman have official YouTube channels that are uploading content from their old TV shows. The PBS show MotorWeek is uploading "Retro Review" clips of their old car reviews from the '80s and '90s and often runs live streams of entire old episodes.
If someone else uploads the content without permission, it's up to the copyright owner to decide what to do. They can 1.) contact the uploader and ask them to take down the video, 2.) file a DMCA takedown request to have the video removed, 3.) have YouTube block it worldwide or in certain countries, 4.) allow it to remain online but take all of the ad revenue from it, 5.) allow it to remain online and share the revenue with the video's uploader, or 6.) do nothing and allow the video to remain as-is.
Years ago when I uploaded a Robert Goulet song to YouTube, I got an e-mail from his widow, Vera Goulet, demanding that I take it down, which I did.