The out-of-the-box "Assigned to Me" filter currently does not include resolved issues in the filter results.

A number of other users have inquired about this and the suggested work-around is to build a custom filter and use the Filter Results gadget.

Many new users to JIRA expect that the "Assigned to Me" does indeed reflect what's in their "inbox" - they do not know intuitively that it excludes resolved issues.

A nice enhancement would be to include an option to include unresolved issues (perhaps in the form of a checkbox on the gadgets configuration screen).