Will some people ever be able to make our dreams visible on a screen? There are many SF-films in which dreams of people can be seen by others on a TV-screen. Don't you have to put so many information gathering devices in a person's brain for this to accomplish, that dream can't enter your brain anymore?
As @AaronWeinberg stated in the comments, just like many other technologies within Science Fiction, the Science Fiction of viewing dreams on screen has started to become Science Fact.

Rebecca Morelle, a science reporter for the BBC World Service wrote an article about researchers in Japan who used MRI scans to reveal the images that people were seeing as they entered into an early stage of sleep.

From the articles I have seen, it looks like the research has been led by Professor Yukiyasu Kamitani, from the ATR Computational Neuroscience Laboratories, in Kyoto.  It seems that the research started in 2005 with an article titled Decoding the visual and subjective contents of the human brain (Kamitani &amp; Tong, 2005) followed by the article Neural Code Converter for Visual Image Representation (Yamada, et al. 2011), follwed then by Decoding visual experience from the human brain (Kamitani, 2012) and then the source of the first linked article Neural Decoding of Visual Imagery During Sleep (Horikawa, et al. 2013)

The results of the first study within the 2005 article demonstrated that


  fMRI activity patterns in early visual areas, including primary visual cortex (V1), contain detailed orientation information that can reliably predict subjective perception.


The 2011 article says


  [T]he neural code converter may provide a basis for brain-to-brain communication of visual images.


The 2012 article says


  Despite the wide-spread use of human neuroimaging, its potential to read out, or "decode", mental contents from brain activity has not been fully explored. In this talk, I present methods for decoding visual representations from fMRI activity patterns based on machine learning techniques.


and the final article in 2013 says


  Our findings demonstrate that specific visual experience during sleep is represented by brain activity patterns shared by stimulus perception, providing a means to uncover subjective contents of dreaming using objective neural measurement.


References

Horikawa, T., et al. (2013) Neural Decoding of Visual Imagery During Sleep. Science 340(6132): pp. 639—642DOI: 10.1126/science.1234330

Kamitani, Y. &amp; Tong, F. (2005) Decoding the visual and subjective contents of the human brain. Nature Neuroscience 8(5): pp. 679—685
DOI: 10.1038/nn1444

Kamitani, Y. (2012) Decoding visual experience from the human brain. Proceeding MM '12 (Proceedings of the 20th ACM international conference on Multimedia). New York:Association for Computing Machinery pp. 5—6 DOI: 10.1145/2393347.2393353

Yamada, K., et al. (2011) Neural Code Converter for Visual Image Representation. 2011 International Workshop on Pattern Recognition in NeuroImaging: pp. 37—40DOI: 10.1109/PRNI.2011.13