It actually happens surprisingly regularly, you usually just don't hear about it because it often happens at the end of the season, between two teams who aren't going to the playoffs. I'm not positive this is the most recent one (although I can't find a more recent one), but here is an example of a tie from 2005:
http://www.Baseball-reference.com/boxes/CIN/CIN200506300.shtml
The 2011 regular season will end during the last week of September. The playoffs will begin on Friday, September 30th with the two American League Division Series. The National League Division Series starts Saturday, October 1st.
The 2013 MLB regular season began on March 31st and ended September 30th. The World Series ended on October 30th.
Continental Baseball League ended in 2010.
Ladies League Baseball ended in 1998.
Canadian Baseball League ended in 2003.
Golden Baseball League ended in 2010.
A-League Pre-Season Challenge Cup ended in 2008.
No. IF you are on a high school baseball team you can have nothing to do with your travel baseball team until the high school season has ended.
International Baseball League of Australia ended in 2002.
In MLB, the regular season started on April 4 and ended on September 30.The final game of the World Series was played on October 17.
Major League Baseball on NBC ended on 2000-10-17.
Major League Baseball on ABC ended on 1989-10-28.