From my point as a WordPress developer, I consider the following plugins quite helpful:
The Debug Bar is a super useful plugin which adds an additional menu to the WordPress backend displaying query, cache, memory usage and other helpful information. Additionally you can also enable PHP warnings and notices when WP_DEBUG is enabled.
With the Usersnap WordPress widget you have found the perfect place for every single piece of feedback. Whether it’s about discovered bugs (hopefully not), change requests or simply new ideas or general feedback.
By adding the Usersnap widget to your site, a little feedback widget is displayed on your website, enabling visitors – or if wished – clients and certain colleagues to provide feedback.
Not only useful for WordPress developers, but for all WordPress users as well. The Simple History plugin displays recent changes made within WordPress directly on the dashboard page.
W3 Total Cache
When it comes to optimizing your website’s performance, W3 Total Cache is your plugin to choose. Optimizing the speed and load time of your website can be quite a challenge. With the W3 Total Cache plugin you can make use of caching.
With BackWPup I’ve found an awesome plugin doing a great job when it comes to saving complete WordPress installations to external services, like Dropbox, S3, FTP servers and many more.