Note that this is taken directly from the Resident Evil 5 game book. Capcom was nice enough to provide a quick history of the franchise towards the end of the book.
NOTE that this is a VERY brief history, and it does not go into detail for each game, etc.
1996
Racoon City Police Department's S.T.A.R.S. team is founded with Albert Wesker as captain.
July 1998
Wesker sends Alpha Team to search for Bravo Team after communication is lost with them in the Arklay Mountains. Alpha Team encounters zombies created by the biohazard in the Arklay lab and mansion.
Wesker's plans are exposed. After his death at the hands of the Tyrant, an unkown virus within his system revives him. He then gathers B.O.W materials and escapes the Arklay lab before it is destroyed. Wesker exploits his apparent death to go into hiding.
September 1998
Former S.T.A.R.S. member Jill Valentine infiltrates RAcoon city.
Umbrella deploys the B.O.W. Nemesis T-Type into the city, and it begins its hunt for former S.T.A.R.S. member Jill Valentine. Jill defeats the Nemesis T-Type and escapes with the help of Barry Burton.
October 1998
The U.S. government decides to impliment a "containment strategy". The president orders a missile attack on Raccoon City, destroying all traces of it.
December 1998
Clair infiltrates the Paris laboratory, only to be captured and imprisoned on Rockfort Island.
In order to obtain a sample of the T-Veronica virus, Wesker attacks Rockfort Island with his own private military force and releases the T-Virus onto the island.
Continuing his search for his sister Claire, Chris arrives at Rockfort Island and finds Wesker.
Claire and Chris are reunited at the Antartic Base, and together they defeat Alexia. They escape in a Harrier jet before the base is destroyed.
2002
Chris and ill take part in the mission to destroy the Umbrella Caucasus Research Facility in Russia. They were successful in destroying a new B.O.W. known as T-A.L.O.S.
2009
Chris Redfield, now a member of the BSAA, heads to Africa on an investigative mission...