The application logging for Exchange Online has been increased from what was once a week out to 90 days. The first announcement was for Message Trace capability was announce going up to 90 days. The announcement was here - http://blogs.technet.com/b/exchange/archive/2014/02/04/extending-message-trace-to-90-days-in-exchange-online.aspx. Additional information is here - http://technet.microsoft.com/en-us/library/jj200668(EXCHG.150).aspx.
Along with that I noticed that the Audit Logging reports have as well been increased to 90 days as well. Read here - http://technet.microsoft.com/en-us/library/jj150497(EXCHG.150).aspx.
Information in general is available in the Reporting Features and Troubleshooting Tools Service Description for Exchange Online located here - http://technet.microsoft.com/en-us/library/exchange-online-reporting-features-and-troubleshooting-tools.aspx.
Remember if you need the data for even more than 90 days, there are reporting APIs available that can allow you to get access to all of this data and store it locally - http://technet.microsoft.com/en-us/library/exchange-online-reporting-features-and-troubleshooting-tools.aspx.