By default there are the FlightRecorderTrace files that you can reference unless you have turned these off which are stored in the Log directory. These are only available for the last two hours (circular files) or depending on the activity there is a file size limit and that depends on the settings in the SSAS instance properties.
You can also enable the QueryLog and store the information in a table and you might already be doing this to use the information to perform your partition aggregations using the Usage Based Optimization.
Here is a list of options that I pulled from this location - http://ssas-info.com/analysis-services-tools - that you might find useful and I also pulled another project from CodePlex that is useful. The SQL CAT team is working on a project similar to the DMVStats for SQL Server that you will be able to use for SSAS 2008 utilizing all of the nice DMVs that are available now (lot of this you can get using the ASSP project on CodePlex, so you should be able to use with SSAS 2005 also).
OLAPQueryLog analysis
Methodology for Monitoring 2005/2008 SSAS Using Profiler trace files
Companion for MS Analysis Server by SQL Minds Inc.
SQL Server Analysis Services 2005/2008 Activity Viewer
ASSP - Analysis Services Stored Procedure Project