I would probably sit and ask myself what the point is for a while.. I think the thought that I'm the last human alive would be tough to deal with for a while, a big responsibility, even as just one individual.
After that I'd sit and analyze survival for the next few decades, kind of like how Zaehet did. Electricity grid would go quick, I'd learn how to set up solar panels and stock up on as many hard drives as I could fill on any torrent I felt was significantly important, and plenty of porn!
I'd teach myself the workings of piloting aircraft, so I could get places faster (not that time would matter much..)
I'd go put my feet up on the presidents desk in the white house and hotbox the oval office like this;
[youtube]NIEnR0nv1a8[/youtube]
I'd go to every famous place on Earth
I'd use every illegal substance in the most irresponsible way
What would I fuck?!
I'd build the coolest houses in a dozen different locations over the world over my lifetime and live at each of them during the year
I'd have to have a dozen main food sources at each place, too, so I'd keep a pretty decent seed bank and stockpile of animals with me all the time when I travelled
I would gather all the best art, cars, statues, monuments, relics, ect. and store them in one place so I could go there and check them out whenever I wanted
I'd learn to play my favorite instruments
I'd gather every gun I could find and store it in a collection and shoot them all the time! Raiding military bases would be the best thing ever!
I'd learn how to operate a wingsuit!
I'd learn how to fly rotary aircraft and fire hellfires at shit
All of this would require a considerable amount of reading, so the existence after the electricity and internet went out would probably be pretty dependent on your access to hard drives and libraries