Do the hole patterns for SNS, NNN and 3-pin (including Back Country variants) cross-country ski bindings match up at all, or do you always need to drill new holes in the skis when installing a different binding system?
The different binding systems are of course primarily designed to provide a standard interface between the binding and the boot, not necessarily to provide a standard way of mounting the binding on the ski.
However that said I believe that the drill-pattern for SNS and NNN are generally speaking compatible, a situation that has some backing from the fact that I could find someone selling a universal drill jig for "Soloman and NNN bindings". I could not find something that ties in the older 3-pin system, but I suspect (but have no evidence for) that the mounting on the newer systems probably reflect the standard pattern of mounting the on the 3-pin system.
You should also be aware that in 2005 the NIS (Nordic Integrated System) was introduced, that uses a rail bonded to the ski that is compatible with both NNN and SNS bindings - so no drilling required with compatible skis.
The hole pattern is the same for NNN and SNS binding systems, but they are placed differently with reference to the balance point of the skis. In other words, the holes don't go in the same spot for the two systems. Plug the old holes and drip hot p-tex to seal them, then drill in the correct spot for your new system.
The three screw holes for the toe section of NN (3-pin), NNN (not NNN-NIS) and SNS bindings match up, but as stated earlier here above, the balance of the ski will be affected when switching from one binding system to another reusing those screw holes. When mounted at the balance point of the ski, NN bindings have the front screw 17 mm in front of the ski balance point; the corresponding distances for NNN and SNS are 59 and 35 mm respectively. Let us suppose the original binding is mounted at balance point. Then, when switching from e.g. NNN to SNS reusing the three screw holes mentioned, the new binding will be 24 mm in front of the balance point thus making the ski tail-heavy with the SNS binding. This is rarely wanted. When switching from SNS to NNN the NNN binding will be mounted 24 mm behind balance point. This may be good for classic skis and perhaps acceptable for skate skis.
The two holes for the rail part of NNN and SNS bindings do not match up between the systems when reusing the three front holes.