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
How it should have gone down:
Subcommander Sela: How are we ever going to be able to make it through the detection grid?
Moderately Intelligent Romulan Officer: Um...we're in space...how about we fly over it.
Subcommander Sela: BRILLIANT! Someone give that man a Romulan Ale, on me!
Also all the maps of the neutral zone are two dimensional.
For example, I can look at a far-away tree through a telescope (visual range), but that doesn't mean I can hit it with a BB gun (targeting range). The starship's sensors have identified the other ship, but all they can do is look at it on their big-screen until it gets close enough for their torpedoes to hit it.
"It's because the plot wouldn't work if they didn't."