Specifically, getting rid of orphaned tables and options after a plugin has been removed.
My two top candidates aren’t much to look at, and (at least to date) don’t include nag screens or adware:
Clean Options, according to its page on WordPress.org “hasn’t been updated in over 2 years. It may no longer be maintained or supported and may have compatibility issues when used with more recent versions of WordPress”, but it allowed me to clean up some leftover options on a WordPress 4.3.1 site.
Plugins Garbage Collector finds orphaned tables and lets you nuke them.
WP Optimize doesn’t address orphaned options or tables, but does display database statistics and includes routines to remove stale data, metadata, transient options, spam comments and other stuff that takes up unnecessary space and cycles.