Are there any widely applicable models for plausible aircraft auto-routing?
I am looking for routing algorithms whose output is the actual path that if set on an autopilot will bring the aircraft through an endpoint at a specific bearing, level and speed


There are indeed models for moving between waypoints: I remember siting on the flightdeck of an A320 and noticing the airspeed increase as we descended towards the airport. I asked the pilot and he responded that this was in preparation for a turn coming up as to not loose airspeed. Not a huge differences perhaps but will make a difference over a year with a lot of aircraft.

Most airlines have company routes detailing which waypoints to use to a destination. To the best of my knowledge, these are fairly standard (you might have  few) and not too weather dependant, unless there is a big storm for instance. One exception to this are transatlantic tracks that are changed daily depending on weather. At least for most flights, possible variations are few and will be in busy airways. Changing airways is normally a larger deviation so it is just good to bare with it, and the weather is unlikely to be considerably better for just a slight detour.


  As a secondary question, do ATC systems have some sort of auto-routing as an aid to operators at busy areas?


ATC have normally no real incentive to cut down routes, at least in cruise. They might help you skip some waypoints and get the aircraft down a little quicker if the airspace is calm during arrival. To also put things into perspective, I was on the flightdeck into a moderately large european airport where we were put first into a hold due to bad planning and then told to speed up after we left it to catch up again. Arlanda airport had something going on however with green approaches. 


  I am looking for routing algorithms whose output is the actual path that if set on an autopilot will bring the aircraft through an endpoint at a specific bearing, level and speed. 


The issue here is that there is no incentive for aircraft manufacturers to release such algorithms to the public. If Airbus uses algorithm A, and Boeing algorithm B, each with a different inputs, you neither would want the other to make algorithm C that works with both inputs and being more efficient. The bottom line however is that everybody remains constrained by the infrastructure already in place that is pretty rigid.