2-D Space: As mentioned under Space Is An Ocean, averted – indeed, one of the major motivations for splicing the ability to better handle the third dimension into people’s brains, and later one of the major reasons why Space Fighters flown by meat don’t exist, is to avoid losing embarrassingly to people who can cope with the three-dimensional, dynamic, always-in-motion nature of space the way it really is.
Consequently, spacecraft encounter each other at any number of arbitrary angles and vectors (except when deliberately moving to dock, when obviously they need to get their airlocks and, if any, spin axes properly lined up), and tend to have arbitrary orientations except when conditions dictate that a particular one is preferable – whether for reasons of technical necessity (solar panels work better facing the sun) or otherwise (what’s the point of being in orbit if you don’t enjoy the view?).
In-system, vessels often do stick close to the single plane that is the ecliptic (because that’s where almost all the planets and other interesting features are), but it’s not all that thin a plane, the usual half-dozen degrees or so of variation in planetary orbital inclinations adding up to a lot of actual space, and it’s certainly not compulsory.
See also the aversion of Old-School Dogfighting.