I want to see how many total hours I have logged in jira. Currently jira shows work log for individual story / sub tasks. But is it possible to show the total amount of work logged in jira by individual developer.
It would be nice if it shows a kind of metrics where work logged against each day is shown.
Edit : can I see burndown chart for individual developer?
One of the free option available is to use the browser extension named Jira Assistant available in below url. This extension has lot more useful features which not only helps to generate report, but also help to log your work on daily basis with notifications, calendar integrations and lot more cool features which helps both managers and team members in their daily activity:
For Chrome users: https://chrome.google.com/webstore/detail/jira-assistant/momjbjbjpbcbnepbgkkiaofkgimihbii?src=sof
For Firefox users: https://addons.mozilla.org/en-US/firefox/addon/jira-assistant/
There is no build in good way to achieve it but the maximum you can take with build in functionalities is following.
Options 1:
Create filter like following JQL:
worklogDate > startofWeek(-1w) AND worklogAuthor = john.smith
Then using worklog "Pie Chart" widget to sum. It is available for standard Dashboard. In "maximized" view it gives table with the numbers. It allows breaking by certain criteria. Then for each user you will need a widget on a dashboard to track which is not convenient.
Options 2:
Use filter like given above to create Agile board and leverage "TimeTrackingReport" or "WorkLog" reports. Please bear in mind that Worklog report can be narrowed by User but does not give much flexibility 
Hope this helps!
will show total time for each day/tickets etc.
You can use query like below in JIRA
project in ("TEST_PROJECT") AND worklogAuthor in ("testuser@testjira.com") AND worklogDate >= startOfMonth()
You can use "sumUp for Jira" plugin
https://marketplace.atlassian.com/apps/1211625/sumup-for-jira?hosting=cloud&tab=overview
its sums up any numeric field values incl. worklogs and displays the sums in the issue navigator, dashboard gadgets or custom fields
You can create a filter with current user assignee and create a board with it and then you can add a burndown gadget to a dashboard to see the chart for each one