I originally had three files: makefile, readme.txt, and hashtable.c in my directory, where I am writing my code in emacs. I noticed that some new files: #hashtable.c#, #readme.txt#, hashtable.c~, and makefile~ have been created. I was wondering what these files were. Are these important, and if not, how do I tell emacs to stop making them? I'm also curious why readme.txt doesn't get a tilde file and makefile doesn't get a sharp file.
The file with the ~ is a backup file that automatically gets created when you save a file. The #readme.txt# is the file being currently edited/in use (i.e., the autosave version). That will usually go away (unlike the ~ file) when you exit emacs normally (if it crashes or gets killed the # files may stay around).
You might find this page about emacs backup files of interest, and this SO question: How do I control how Emacs makes backup files?
You can prevent backup files from being created with this:
(setq make-backup-files nil)