I am having a problem with a couple of mov-files I received from someone else. I see only a black screen, when I drag these files into the Timeline of Vegas (version 8). I can see and hear the audio, however.
Does anyone have a solution?

I hate to be the bearer of bad news but odds are that the only solution is to upgrade to a newer version of Vegas. I have Pro 8 and it will not read mov files from, for example, an iPhone or an iPad while Pro 10 will do it.

Nevertheless, it is an answer that sounds reasonable.

You could also in the short term use a video converter to change the mov files to a format your Vegas can use, since you only have a few of them.

I would encourage getting an upgrade to the newest version of Vegas as the long term solution.

Shortly after I purchsed a new Canon XA20, three months ago, I checked, whether my Vegas Pro 8 would accept the files of this cam. And it did. So my ancient version should not be the problem.
The first thing I tried was converting the files, but this failed. Several tries in several converters.
Earlier today however a "version-12-user" converted them for me in Vegas and now I do see the moving pictures.
Problem solved.

Shortly after I purchsed a new Canon XA20, three months ago, I checked, whether my Vegas Pro 8 would accept the files of this cam. And it did. So my ancient version should not be the problem.

In that case something has changed in your computer and my guess is that QuickTime did an unwanted update. It's well known that newer versions of QuickTime Player mess up the ability of Vegas to read MOV files. I know this because it's happened to me. I use 7.6.8 and it works for me with older versions of Vegas. Try that version or go back even further to 7.6.2. If it does work for you, disable the option in QT player to automatically download and install newer versions.
You can find both of these at Download Old Versions of QuickTime for Windows - OldVersion.com (http://www.oldversion.com/windows/quicktime/)