Every space setting has its conquerors. They may vary in effectiveness and track record but they all want the Galaxy (or at least the Local Arm). Nothing gets a group of players talking and planning like an invasion whether they are joining the defense or figuring out how to jack the local bank during the carpet bombing.
First invaders need a reason for not playing nicely with others. In Traveller the Aslan want your land. The Vargr want your stuff. The K'kree want you to file down your teeth and eat salad. The Klingons wanted it all because Klingons were the greatest (damn those Organians!) Their reasons will color their methods and the nature of their occupation. The K'kree, for example, don't really care how their subjects lead their lives as long as they don't eat meat. Similarly if you move out of the way of the Aslan landlords they'll let you be. More mercenary invaders may let you alone aside from going through your pockets every week or so or may start strip mining your world down to the basalt. I suspect the Klingons were fond of making their subjects build big monuments to Kahless.
Invaders used to after resources like water or metal or food till some wise ass told them they could have all that in their own solar system through terraforming and asteroid mining for much less trouble. Unlee they want unobtainium and you have it that motive is out of favor currently.
Technology and numbers will also shape an invasion. Do your conquerors win by technology advantage? Are they somewhat backward but carry the day through numbers and savagery like Warhammer's Orks? Do they strike with precision on blast everything in sight that looks except Tom Cruise? This can have a big effect on property values and player character health.
Storytellers often go with the shock and awe style of invasion. There are other more subtle ways. Invasion of the Body Snatchers dealt with alien plants secretly replacing humans with doppelgangers. Mind control is a hot item among those acquisitive aliens who don't like being shot at. A secret invasion can make for a lot of paranoia. Who is on the players' side and who is the Enemy. For added laughs keep pulling one player out of the session for 'private' discussions.
Note that an invasion can also benefit from sabotage. This is more likely for the high tech invaders than the win by sheer numbers crowd. In Battlestar Galactica (both versions) the Cylons disabled the human warning systems and struck with total surprise. Just because you expect an easy win doesn't mean you can't make it easier and covert operations like this are something a player group can could run across and defeat and sound a warning (not that anyone will believe that scruffy bunch.)
Finally the exact attitude of the invaders towards humans (or whatever) should be determined. Are they to be assimilated, absorbed, dissected, enslaved, brainwashed or simply exterminated? It's not as simple as it sounds. If you want a subject planet but don't want to pay a huge garrison you might want to relocate or kill all the parent units and reeducate the young (future consumers/consumables!)