Randomly losing CMD+V (paste) functionality I am randomly losing CMD+V functionality. Is there a shortcut which might trigger this? So that the keyboard goes into some kind of different mode?

I am working with cmd/shift/option a lot in gfx apps, like Illustrator. 

I thought, maybe the CMD-key is broken, but this happens with both CMD-keys.

After some time using the system it starts to work again.

I am on Mountain Lion, to which I recently switched, never had this problem prior to Mountain Lion.
I had the same issue, what I found was that using a Software called ShareMouse, and when it crashed, I lost my Cmd+v functionality; I then forced ShareMouse to close, and cmd+v returned. 

You may be experiencing this issue with ShareMouse, or some other piece of software.