Something that has occured to me in the past whilst thinking about this is that given the miniscule evidence our species and civilisation will leave in the geological record, can we really be sure that no other short-lived civilizations have existed previous to homo sapiens?
Well, that was an interesting article. Flawed, but interesting.
It's not clear how the Earth will end up, since human population reduction looks unlikely barring catastrophe - intentional or otherwise.
However, I think humans will very quickly (< 100 years) spread throughout the solar system, and eventually into the Oort cloud. At some point, sooner or later, humans will also become an interstellar species.
Human artifacts may or may not always be visible on the Earth, but they'll be easily visible on the Moon until it gets eaten by the Sun.
On that note, it's worth mentioning that life on Earth is roughly 4/5 of the way along its timeline. Earth will become unbearably hot in well under a billion years, regardless of human contribution, due to increasing solar luminosity...