I remember when the International Space Station's Expedition I crew arrived in November 2000 that news media said it could mark humanity's permanent occupation of space. That may still hold true, although it happened a generation before it probably should have. When I read that, I remember thinking that we missed marking one milestone for our permanent robotic presence in space, three years earlier.
On September 11, 1997, the Mars Global Surveyor probe reached Martian orbit. Since then, humanity has had at least one satellite in Martian orbit. Three are operating right now and more are planned, from multiple nations and not just the US. We'll never leave.
Somewhat surprisingly, we may also have achieved permanent presence on the Martian surface. In early 2004, two rovers landed on the surface, one of them is still working and making important discoveries, and an even more powerful one is set to land there next year. If it doesn't crash, I think it could last long enough to be there when more landers arrive.
So where else? The moon's had lots of visitors, but most of them were short-lived. From Japan'sSelene mission in 2007 onward though, there's lots of overlap that shouldn't end.
I thought figuring out the start of permanent earth orbit would be hard, but not so (and I'm not counting dead probes, btw, a permanent presence requires operational satellites). Looks like the prize goes all the way back to 1958 with the fourth-ever satellite, Vanguard I, which lasted until 1964. The 1962 probe Alouette operated for 10 years, with countless overlaps since its launch.
My guess is that's it, so far. We have operating satellites at Mercury, Venus, the asteroid belt, and Saturn, but none of them will live long enough to be working when replacements arrive. A probe just launched to Jupiter, but radiation makes that a hard place, and it'll be many decades before we get a permanent presence.
As for future milestones, I think Venus will be the first. A Japanese mission got screwed up going there and is mostly crippled, but the first really operational orbiter that gets there will make things permanent, and I'm sure it'll happen within 10 years. The lunar surface won't be that hard either, maybe 15 years.
A proposed lake explorer on Saturn's moon Titan could get there in the 2020s and last long enough to see a Saturn orbiter years later, so 2020s or 2030s for Saturn. The 2040s for Jupiter, arrival for either a distant weather satellite or a communications satellite to relay info from short-lived probes messing around near its major moons.
I've been foolish enough to speculate this far, but now I'll stop, with no guesses about dates for permanent balloon platforms on Venus, permanent anything near Mercury, the asteroid belts, or elsewhere outside of Saturn and Jupiter. This all assumes no near term fiscal collapse or long term Singularity.
Pretty impressive stuff, overall. The human space program may have stalled out in the last 40 years, but what we've done to get our presence beyond earth has not.