In addition to all of the above that applies to beginners, start writing file-listers :)
Say, write a program that lists all the files in your home directory, sorted by date, sorted by size, grouped by file-extension ... oh look, search a group of directories for movie files, of at least 1mb, sorted by date ... things like that
And I just want to say, keep track of which exercises you do, put your efforts into version control -- its amazing to be able to revisit your code 1, 5, 10 years later