If it was shot on regular video cameras, then no, you can't have it in HD because you're just upscaling a regular image, same as playing a regular DVD on a BD player.
Many modern TV shows are shot on HD digital cameras, such as BSG and the final years of Star Trek Enterprise, so BD lets you see lots of stuff you can't see on the down-res to standard DVD.
Film is dependent on the stock it was shot on, how good the original picture was supposed to be (Clerks, for example, will always look like it does), and the age of the source. A film from 1996 looks better than one from 1966 most of the time. However, a good restoration, such as has been done with the Bond flicks on BD, can make it look so good you won't believe your eyes.
When it comes to HD, think of this...when you take a picture with a 5MP camera, doesn't it look better than a 1MP camera? Of course it does. Use those digital cameras to take a picture of a photograph. The 5MP camera's pic will look better than the 1MP's. That's basically how they convert film to video, HD or standard--you scan each frame at a given resolution. Scan it at 1920x1080 (or higher) and it's HD. I say higher because when you see a movie at a DLP theater now, it's not 1080p. I think the res is 4x higher in each direction, so 16x more pixels than a 1080p display?