As the subject already says: I cannot connect to folders like 'Video's'.
Other folders names works fine but with the folder 'Video's' it keeps asking for a username and password but is always fails.

What happens if you omit the apostrophe (videos instead of video's) or replace the apostrophe by an underscore (video_s instead of video's)?

When i change the name of the folder, I can connect without a problem.
As i am streaming from WHS 2011 the standard folder for Movies is Video's (which cannot be removed) so i would like to keep the original structure.

Small update: I can mount the shared folder 'Video's' on a usb folder named Videos.
but this isn't quite what i want.

As a rule, punctuation in file names should be avoided as it can cause compatibility problems - no matter what the world according to Microsoft thinks
Andy

I know, but as I said, I can not change the name or delete the folder (not in the official way) so I'll have to try something.
I don't want to make a second folder 'Videos'.

I do not understand your problem. You obviously use a Dutch Windows. On my PCs I see Video's indeed, but on my Mini Gebruikers become Users and Video's become Videos and the Videos folder is fully accessible from my Mini. (I shared Public / Openbare folders on my PC).

And as a (maybe redundant) solution create a Videos subfolder in the Video's folder, put your all video files in that subfolder and share that.

I am using the dutch version of Windows Home Server 2011 and the Standard folder/share for Movies is Video's. I can not change or delete this share.
Therefore my question is: how can I logon to a folder named "Video's"?
A subfolder in the folder Video's is not an option as I cannot access the folder Video's.

Windows Home Server 2011 obviously causes more issues, you are not the first with WHS 2011 problems on the forum.
Can you create a Videos folder next to Video's folder and just do not use the Video's folder? Why stick to the rigid WHS file system at all?

Duivel's solution is right
If you create a new folder called videos (anywhere in the file system) and share it out as videos then you won't need to think about the video's folder - the new share doesn't need it.Try it and see
Microsoft need to learn English - video's should not have an apostophe for a plural
Andy