You should backup any files that are important to you, but each person will have a different idea as to what is "important" and what is not. My view is that the most critical files are data files that you've created. As jlightner pointed out, if your server crashed, it's relatively straightforward to resinstall the operating system and various applications (eg, Oracle). However, if your users' data is lost, there is no way to recover it unless you have good backups. I don't think it's possible to provide you with a detailed list of which files you need to backup (after all, we can't see what's on your system) but clearly you would want to save the Oracle database files (this includes the physical files that contain the tablespaces, also the archive logs, etc) plus any user data.
Note that Oracle has its own utilities for backing up the data -- those files should be backed up regularly (ie, daily) and moved off site. At the risk of telling you what you already know, here's a very brief
cheat sheet for running Oracle in archive log mode.