So weird that you mention that, it's a thought I consider so very often! We piece together the ancient past with tiny little bits and pieces (like Lucy's missing bones, or the occasional rock tools or ceramic fragments) and then we just do our best to guess and "fill in the gaps". Considering Fermi's Paradox (I don't want to open that can of worms, but there's a whole new interesting line of inquiry) I think the destruction of humanity is pretty well inevitable, it's just a question of when?
Given the vast distances between the alien civilisations that hypothetically populate the galaxy and (assuming FTL travel isn't possible) it might be millions of years before the alien archaeologists (who will most likely be sentient self-replicating AIs) find the remnants of our civilisation. I wonder what will be left: they say plastic takes hundreds of years to biodegrade but if all life on earth (including bacteria/fungus) is destroyed by some nasty nanotechnology/nuclear/gamma-ray burst, then plastic will be around even longer, perhaps longer than even stone/metal statutes and buildings (which will be destroyed by simple erosion or chemical processes). This is all hypothetical nonsense, but there's actually a really good book about this called The World Without Us by Alan Weisman.. Or at least it explores some of these ideas.
I always think about what would happen after first contact. In reality, a civilisation who contacts earth would be far more advanced than us, perhaps millions of years more advanced: they might perceive us as monkeys almost, perhaps they are observing us already!!.. watching, waiting, dreaming.. [ph'nglui mglw'nafh Cthulhu R'lyeh wgah'nagl fhtagn].. (before I continue this, please ensure you strap on your tin foil hat so George Bush can't detect our orgone energy). In movies they always want to harvest us for food, or kill us because they're "evil" or take our resources. In reality, an advanced (most likely non-organic) civilisation capable of space travel would have practically infinite resources by this stage and would have very little malevolence toward us apart from perhaps zoological curiosity.. keeping us as pets or something, or wanting to catalogue all the plants and lifeforms etc.
But I think the only resource that would actually interest them is our art, music, literature, etc. That's the only thing that we (as humans) could possibly offer another civilisation, the only thing that would be useful or novel to them. Everything else they would already have plenty of. So when the mothership lands, don't worry about them nuking us, eating us, or taking gold from our banks: I propose it's far more likely they'll head straight the Louvre or perhaps abduct poets, artists or game developers! lol. @ben
But what would the alien archaeologists find, and what would they think? Lol, imagine if all they manage to recover is a couple chunks of plastic; actual hard drives/floppy disks in someone's basement. The only files recoverable are a copy of Wolfenstein3D and a CD of Encyclopaedia Encarta 97, mostly corrupted except a few entires about WW2. The question is still unanswered, but I keep thinking about it. Given a set of misc objects recovered, what would the alien civ conclude about us? It's hard as well because we always automatically anthropomorphise the hypothetical aliens.. in reality (due to cultural differences, space radiation poisoning and millennia of robot inbreeding) they're probably only interested in taking all the matter in the universe and then forming it into small strange crystallised four-pronged tetrahedrons and truncated ellipsoids which can then be tessellated together into a colossal structure composed of all the matter in the galaxy, constructed purely for their own unfamiliar spiritual/cultural aims.
Apologies for the wall off text, it's really obnoxious but I'm procrastinating at the moment.. I'm actually developing a game myself in AGS (a point-n-click adventure game) as part of my uni course and doing anything I possibly can to avoid the task at hand.