ETA: Just in case anyone is confused - I follow logical time, so the years that production "skipped" are included in my timeline, which is why events that aired in 2014 are noted as 2016 in the timeline.
1998 - It is around this time that Dean leaves John and Sam to hunt a banshee in Orlando, Florida, while he takes a roadtrip on his own. He meets Lisa Braeden and has a bendy weekend.
2005 - Sam starts his final year at Stanford. He is happily living with Jessica.
2006 - It is in September that Sam meets Andy, a fellow Special kid who is able to command people to do what he wants, solely by talking to them.
2007 - Sam and Dean hunt cases that we never see. Sam, no doubt, worries greatly about his brother and the deal hanging over his head. Meanwhile, Dean, most likely, tries to come to terms with this being his last year on earth.
2008 - Sam hunts with Ruby in a revenge fueled mission to kill Lilith. Meanwhile, Castiel is part of a battalion waging a battle against Hell in order to raise Dean Winchester from perdition.
2009 - This might be when Sam and Dean end up hunting a god who takes the form of Paris Hilton. Castiel deals with the aftermath of rebellion against Heaven.
2010 - Dean lives with Lisa and Ben Braeden, fulfilling his last promise to Sam. Castiel deals with the fallout of Michael's death in Heaven, which has lead Raphael to be the sole surviving Archangel.
2011 - This might be around the time that Bobby is trying to get out of his deal with Crowley. Dean tries to balance living with Lisa while knowing that Sam is alive. Dean is beginning to suspect that there might be something wrong with his brother. Sam's body is hunting with the Campbells. Sam's soul is still in the cage. Castiel is fighting a civil war in Heaven against Raphael.
2012 - Dean and Sam have to deal with a couple of high powered witches having a lover's spat. Meanwhile, they are hunted by Leviathan. Castiel has amnesia and believes himself to be human with healing powers. He's found by a slightly insane religious woman who decides to marry him.
2013 - Sam drives aimlessly around the country, trying to come to terms with Dean's death. This might be around the time that he accidentally hits a dog and freaks out at a local vet in Kermit, Texas, because he's having a really shitty life and he can't stand the thought that he might have accidentally killed a dog on top of all his other perceived failings. Meanwhile, Dean meets Benny and tries to find Castiel in purgatory, while Castiel tries to keep Dean safe by staying the hell away from him.
2014 - Sam and Amelia move into a bungalow together after a forming a relationship based on grieving their dead loved ones. It's super healthy. In Purgatory, Dean, Cas, and Benny near the human-only exit portal. Castiel is no doubt trying to enjoy is final few days with Dean, while Dean is focused on keeping all three of them alive so that they can all escape together and be happy.
2015 - I'm not sure of the date for this section of the year - but this could be around the time that Castiel, now human, discovers a case while working at the Gas'n'Sip. He calls Dean, who comes out to help - leaving Sam, who is also Gadreel, at the Bunker to help Kevin with his research.
2016 - Dean is no longer a demon, and the brothers are hunting together again. We're not sure what happens on this exact date, or even close to it... but in Flint Michigan, a girls' school decides to mount a musical production based on the Supernatural books by Carver Edlund.