Hmm. I've not seen a direct list of apps that require root access, but I'm sure there's one out there. Look at some of the posts in this forum, also at XDA. Often you can get a good idea of what's out there from reading threads that deal with what you're trying to achieve or fix.
I've read your posts in other threads about being new to rooting. Did you have a particular intention when you rooted? Sure, I futz around with custom ROMs once in a while, but my main purpose in rooting was to do full backups of my system. Not for the obvious reason, mind you, but so I could (1) dump the Samsung and VZW bloat, and (2) move my Angry Birds to another device. The only way I've found to move my progress is to backup the app and its data with Titanium. All of the apps that I have used that require root access have been utilities of some kind. Remember that just because your device is rooted, you don't have to use only apps that require root access. Sometimes my rooted S3 has just Titanium and FoxFi that require root.