Really depends on the web host and what ownership is set on the directory, there is no one answer for that question. If the thumbnails are regenerating without errors, you should be fine as is.
The web server needs to be able to write to the directory. The web server will be running as a different user than the user you log in to the server as, 777 is generally considered by be insecure, but could work, as could 755.
Safest plan is to contact your web host and find out what user name the web server runs as and then chown (change owner) of the uploads directory to that user. You can then set the permissions to 755 in most cases.