How can I set custom notifications? I have a Samsung Galaxy Nexus running ICS, and I want to be able to set individual sounds for various notifications (Gmail, Facebook, texts, etc). 

How can I go about making that happen? I looked in the sound settings, and that only allows me to change the default notification sound and my ringtone.
Typically the apps themselves will need to provide a setting wherein you can pick a notification sound to use. I am not aware of any global settings that will allow you to set per-app notification sounds.

As an example, in Gmail you can go into the settings (use the overflow menu - the 3 vertical dots - and select "Settings") and select an account from the list. Then within the account's settings tap on the notification setting right under the "Email notifications" checkbox. This will allow you to pick a different ringtone for emails on that account.

You can then repeat this process for any other apps you have installed.