<p>There is a 3D desktop printer <a href="https://en.wikipedia.org/wiki/RepRap_project">RepRap</a> which can print most of its own components.</p>

<p>Assuming each printed printer will print the next one and so on. Are there any limitation how many times this can be achieved?</p>

<p>For example somebody printed for me printer and I do the same for my friends and they do the same for theirs. Can this go forever (since 3D model stays the same), or there are any serious side-effects/disadvantages of doing that continuously?</p>

As long as you maintain each printer and keep a proper calibration, go for it, this is what they were designed to do, I've even made replacement parts for myself.
Unfortunately the
RepRap project just shut down on 1/15/16
due to their lack of sales.
I have a reprap that came from a reprap, and has made another reprap.
Just make sure that when printing out the pieces for the next you are properly calibrated, otherwise the next machine might be built crooked;
Your only limitations will be the electronics pieces and the small amount of hardware that you will need to buy.