There will come a time when a webpart fails, your site is displaying an error, and you can't do anything on the page.
You'll want to remove the webpart that is causing the problem but if you look at the error page above, you don't even have a Site Actions menu. To get around this, you have to add a query string. Go to your URL and append '?Contents=1' to the end as in the next image.
Now, this will take you to the Web Part Page Maintenance page. As you can see, this page will list every webpart that is currently on the page. Select the webpart that you believe is causing the problem by clicking on the checkbox and click on the Delete button.
NOTE: The delete button simply removes the webpart from the current page, so you don't have to worry about deleting the webpart from all existence.