There are several scenarios that have proven to be particularly fun and popular within this genre.  There is, of course, the typical 1v1, 2v2, and 3v3 duel scenarios which is the basis of the Star Control "SuperMelee" mode.  Here are some others...

Same as above, with three sides.  The 3-player dynamic that game designers are aware of works particularly well within this genre.

Base defense.  There is some type of "base" that provides a defensive advantage to those holding it.  The two sides endlessly respawn as they trade periods of controlling the "base" (whatever that may be).

Star Fleet Battles called it Space Hockey, Subspace called it Powerball.  There is a goal at each end of the map.  There is a puck/ball.  The player holding the ball loses his primary weapon, which instead passes/shoots.

This last one is a little more complex to describe, but creates a very dynamic situation that results in all kinds of crazy things happening.  It's from SFB and is called "The Circle of Death".  Don't discount it just because it is a favorite SFB scenario, like that South Park episode ("Simpsons did it!!!") SFB is 40 years old and has literally hundreds of scenarios, it would be hard to work one out that doesn't already exist there.  In the Circle of Death there are 4-12 players or so (6 in the orignal SFB scenario).  Each player is randomly assigned a target (icon over their ship, glow around them to ID, whatever looks the coolest).  You may only damage the player you are targeting, or the player that is targeting you, and are immediately removed from the game if you damage anyone else.  You don't know which player is targeting you.

While there are many potential scenarios within this genre, these are the ones that have proven to be the absolute most fun and most popular in similar games.