All the Civilization games that I know of have the option to let you keep playing after the win condition is met, A.K.A. the "Just One More Turn" button.
Dwarf Fortress has no win condition and can be theoretically infinite but most games eventually end by a series of things going horribly wrong. Rmember: Losing is Fun!
edited 6th Oct '15 4:47:19 PM by Elle
Galactic conquest games like Galciv, Stardrive 2 and Master of Orion series won't end as long as you don't kill off everyone else or wipe out the "final boss" alien homeworld, but these don't require much management once you've conquered most of the galaxy and no one dares attack you.
You can also try building simulations like Sim City series and Cities XL. These tend to never end as well as you build the city. Tropico might work as well.
edited 7th Oct '15 1:15:09 AM by Malco
My DA account... I draw stuff sometimes!
Yeah, I'd recommend city builders. Master of Olympus I recall was really good! And complicated. So very, very complicated. I'd like to pretend I got my ass kicked in them because I was like in middle school, but the fact is that I'm just not good with that kind of game.
Oh, you might check out Stars Beyond Reach by the AI War guys. Or just AI War. 
So I used to enjoy RTS and 4X games as a kid, and am getting back into them now as an adult. However, nearly all of these games always have a condition at which the game ends: a timer, a win condition, etc. I would love to play a game that just goes on indefinitely, ruling my empire through the ages. (Would this count as a sandbox? I don't know, lol.)
Are there any such games out there? Preferably sci-fi or fantasy, or ideally both in one.
Thanks!