I don't play the guitar; I play the mandolin, but as such I can play the guitar if I want to, so I'm gonna answer anyway
The first songs I learned, which are a bunch of really simple tunes you can play and sing at the same time (singing them convincingly is of course a different matter):
Conway Twitty - Lonely Blue Boy
James Carr - Pouring Water On a Drowning Man
Aretha Franklin - Running Out Of Fools
Last song I learned was a while back. I think it was Inside Out by the Traveling Wilburys. I don't really take playing very seriously anymore though - just treat it as a bit of a laugh, or a way to get a free pint if there's an acousitc night on down the pub.