Thank you all for that valuable input And a special thank to Tempest Fennic for that link, and to Kamikasei for the weird technology suggestions. Yes, it's true I don't actually have to go with the "humanity wiped out today" scenario, but could make us survive a bit longer. Not sure yet...
It's still on the brainstorming phase, but the players are supposed to be born on this world. Like I said, it is supposed to be a traditional fantasy world, just with the "future earth" twist. Exactly how I am going to explain some things, I am still working on, since gods and magic are supposed to exist. Maybe those things existed all the time but we modern people neglected and forgot about them. Or maybe humans somehow evolved to god-like beings that are now being worshipped by the creatures they have made into their (old) image. Or maybe we left in generation ships, got caught in some pseudo-scientific time-twist thingamabob, got back to earth millions of years later (where a lot of entirely new species had evolved) and then lost our memory of our old civilisation.
In short, it doesn't have to be too realistic; after all, the hyborean age as well as Middle-Earth are supposed to be our distant past (and not even all that distant, at that), and the Dungeons & Dragons setting Mystara is set on Earth about 150 million years ago (in fact, doesn't it even say in the old golden Immortal box that the setting is our world millions of years ago?).
Like I said, I understand that there will not be any possibilities of mysterious undersea city ruins or the Statue of Liberty, unless I go with Kamikasei's suggestion with futuristic materials that might survive for that long. I was really just wondering if anything small could survive - anything from nuclear waste to fossilized footprints with the Nike swoosh (that was a good one )
Anyway, thanks for your input so far.