Is there a way to change the sounds when you receive a text, email, etc. I have done this with my ringtones, however I would like to change the other sounds.
The only one you can change is the text alert, and then only to one of the 6 sounds that are in the settings menu. Other than jailbreaking your iPhone there is no other way to customize those alerts.
If you've jailbroken your phone and you have SSH access:
The sounds are in /System/Library/Audio/UISounds/
They are aiff, rename them to .caf and replace as needed. You can listen to them with Quicktime or QuickLook to see what they are. You can replace the Mail Received one if you like, you can change any sound you want.