The question is pretty much in the title. I would like to have the same artboard in illustrator as three different pages in a pdf-file, each page should have different layers visible. Is this possible to create automatically? How?
If I'm understanding what you want, I think the quickest way is to just make 3 separate PDFs from your .ai file, with the desired layers showing in each. Then combine the 3 files into one PDF using Acrobat Pro.
Edit: As for "automatically", not sure there's a way to automate this process, because saving a PDF (or jpg) with "Use Artboards" checked will still just create separate files from each artboard.
If you have a small number of layers, or will not be making any/many revisions, I think DLev's answer is great.
But if you have a more complex layer system in place, and/or will be doing several revisions, I think Rsiel's comment is dead-on. All credit should go to them, but here is a little more detail about what that process looks like.
Set up your Illustrator file with the objects on the layers however you want
Save this Illustrator file.
In InDesign, create a document with the same page size as your Illustrator artboard size, and as many pages as you want variations of layer on/off configurations. Then,
File > Place and select the Illustrator file you just saved. In that box, make sure you place a checkmark next to
Show Import Options, then click
In the next window, click the
Layers tab, and select the layers you want visible on the first page, then click OK.
Repeat those steps as many times as necessary for your desired layer on/off variations, and then you'll have an InDesign document with each variation on a new page.
Then, go to
File > Export, and save your InDesign file as a PDF.
Now, whenever you update and save your Illustrator file, just open the InDesign file, update the links, and export a PDF. You don't have to re-select the layers all over again.
NOTE If you change your layer names or layer order in Illustrator, you will have to re-place and select layers in InDesign like you did above. If using this method, it is highly recommended to determine layer names and sequence prior to setting up the InDesign file.
DLev's technique is the best manual method.
Thomas Byrne created some scripts for this, based on Matthew Ericson's original. I believe this is the most automatic way to do it.
Source: http://www.tbyrne.org/export-illustrator-layers-to-svg-files (it supports PNG8, PNG24, PDF, EPS & SVG formats)
Commercial Add-On: https://creative.adobe.com/addons/products/2955#.VSvrwfnF_uM