There are several places Recent files are found -- application File menus, Finder Go menu, Apple menu, etc. Since you said Finder I'll assume the latter two are what you're talking about [it would help if you were more specific]..
Apple menu > Recent Items and [Finder] Go menu > Recent Folders both have a Clear Menu command at the bottom of the menu -- in theory that should clear out older "recent" files, though apparently it may not always work as intended.
In System Preferences > General you can turn off Recent items [set to None], and you can add certain folders to the Privacy tab in System Preferences > Spotlight, but then you won't see any new recent files [and the Spotlight method may impact your ability to do searches]. Recent item lists have always been a little flaky, I wouldn't depend on them too much -- you could instead create aliases to locations you use frequently, for quick access..