We use Jira ( plain jira, no greenhopper ) for project/task management and a separate system for time tracking.
How can I run a report to extract all the hours I have worked in the last week?
You can create a custom filter with a custom search query:
project = "My project" and timeSpent is not null and updated > startOfWeek("-1") and assignee was CurrentUser()
More information on JQL is here - https://confluence.atlassian.com/display/JIRA/Advanced+Searching#AdvancedSearching-Updated