Copy all files except from some certain folders.
 

At the moment I'm using:
"cp -ap . /destination-folder"
to copy everything from the folder I'm in to another folder.
That works.

Is it possible to cp everything except:
folder1/
folder2/
in the current folder I'm in?

You need something that you can easily --exclude things with. Two tools come to mind: 'tar' and 'rsync'.

As implied by unSpawn, there is (unfortunately) no --exclude option for cp.
Other solutions include:

1. cp everything, then rm at the destination
2. write a short script to call cp, skipping those dirs