Great topic! It's always interesting to see which games other people have; there always seems to be at least 1-2 that I've not seen or heard of before.
Indeed,
bbmike's list is no exception. I'm pretty sure you own more space 4x games than I do, incidentally. (Maybe I'm just a little choosier? Yeah, let's go with that...
)
Anyway, here's what I've got (same caveat, the list may not be comprehensive, etc.):
Armada 2526 Gold Edition
Astra Exodus
Birth of the Federation
Children of the Galaxy
Dawn of Andromeda
Distant Worlds: Universe
Dominus Galaxia
Endless Space - Definitive Edition
Endless Space 2
Final Theory
Galactic Civilizations 1
Galactic Civilizations II: Ultimate Edition
Galactic Civilizations III
Horizon
Imperium Galactica II: Alliances
interstellar Space: Genesis
Lord of Rigel
Lost Empire: Immortals
Master of Orion 1
Master of Orion 2
Master of Orion 3
Master of Orion: Conquer the Stars
Pax Imperia: Eminent Domain
Polaris Sector
Predestination
Reach for the Stars (2000 sequel/remake)
Remnants of the Precursors
Space Empires IV Deluxe
Spaceward Ho! IV
StarDrive
StarDrive 2
Star Ruler 2
Starships Unlimited 3
Stars in Shadow
Stellar Monarch
Stellaris
Sword of the Stars Complete Collection
Xenia's Ark
Space 4x-"like" games:
AI War: Fleet Command
AI War 2
Conquest: Frontier Wars
Emperor of the Fading Suns
Gemini Wars
Sins of a Solar Empire: Rebellion
Star Wars: Empire at War - Gold Pack
Starpoint Gemini: Warlords
My all-time favorites: Stellaris, Birth of the Federation, Distant Worlds, Armada 2526, Imperium Galactica II, Galactic Civilizations II & III, and -- somewhat to my chagrin -- StarDrive 2 (hey, the numbers don't lie).
Wow thats is alot invested in the genre, as you can see from my list I'm a complete and utter beginner when it comes to space 4x
Stellaris
Thats it thats my list
You could definitely do worse than start with that one.