In most Star Trek scenes in which two or more ships meet, they'll face each other on the same plane, as though they were traveling in two dimensions, not three. This is physically unrealistic, but it's the only way to avoid the impression that a lot of ship captains are smashed drunk.
Lately, I've been re-watching Enterprise, the last Star Trek television program. The writers corrected many of inconsistencies from the previous shows. You can occasionally see ships meeting each other in non-parallel fashion.
-via Geek Tyrant