I recently decrypted my home directory by making a backup of my home directory, deleting the directory, and then replacing it again with the backup (followed a guide). Ever since, I can no longer run standard built in software like Iceweasel and LibreOffice without root access. Whenever I try to open the programs, they give me some sort of error like "Iceweasel is already running" (which it isn't). But when I run them from the command line with sudo, they work fine. I think it has something to do with the permissions of my home directory, not entirely sure. I'm wondering how I can give my user permissions to run all the software in my home directory without having to use sudo in the command line. I'm pretty sure when I was moving my home directory around, it messed with the permissions. (This is just a guess, not sure why I need root permissions to run these types of software).
If you fiddled with your home directory, you needed root to get at the /home directory that contains it. Possibly your home now contains some stuff owned by something other than you, that the sudo obviates.
An aggressive approach might be
sudo chown -R myname:users ~myname
A more cautious person might do
find ~myname \! -user myname to look for such things, then fix them.
Programs saying "already running" tend to be pid files that aren't cleaned up, or unix domain sockets left about.