I do my own custom factions that were created over a series of years for roleplaying purposes (And possibly a novel ro two... eventually)
I have three that I regularly try to make in games:
The Terelain Star Kingdom
Officially named the Third Kingdom of Terel, it is an ancient civilisation of bipedal ageless felines. Arrogant and aloof they are meant to be played as highly isolationist with a primarily defensive mind-set - I'd hope to give them a population growth penalty so they have a small slow-growing population that they have to protect. On the flip-side they'll be very good at research and have a high soldiering skill to represent both the highly trained nature of their army and their advanced technology. In general they would do poorly in war against a foe with considerable numbers on their side, and as such their war-time strategy would be to leverage an early technological advantage to attempt to cripple possible future enemies (Drengin, Yor, etc)
The Xin'Ta'Faxi Imperium
Fragile of body and telekinetic, they are master shipbuilders and architects and in their original universe their city-planet homeworld was one of the major hubs of interstellar civilisation. as such I often give them bonuses to social and military production, ship health and minor bonuses to influence or diplomacy. Penalties would be to soldiering and research due to the power of their monolithic religion, the Church of The Guardian. They excel at blockading and planetary bombardment, but they fare poorly against other races at groundside combat.
The Sithrimni Collective
A race of Telepaths hailing from the twin planet of the Xin'Ta'Faxi homeworld, they were driven from their home system in the early days of space travel by the Xin'Ta'Faxi. Pacifistic and peaceful, they would gain large bonuses to influence and morale but significant penalties to soldiering, diplomacy and military production. Very much a race intended towards diplomatic and influence victories, they wish to peacefully expand the influence of their group mind in order to spread peace and understanding across the galaxy. Despite the fact that forcing individuals into the Collective is forbidden they are generally viewed with mistrust and suspicion by other races.
Generally the races I make tend to either be bad at war or be defensively-minded as a handicap. I need to develop a culture and economy capable of making up for poor skill at war.