I would like to shrink the size of a partition containing an Ubuntu distribution and files. Is it safe to assume that I will not lose or corrupt any of the files as long as I don't make the partition smaller than the amount of data that is currently on it? I am planning to use GParted from the Ubuntu LiveCD.
As @David_Collantes said, make sure do backups beforehand, just in case. That said, I've never lost data using it, but I would also recommend that you not try and shrink too close to the amount of data on the partition - leave at least 10% free if you can. This will help the filesystem deal with fragmentation and also allow for the reserved 'system space' to not be immediately in use.
Watch out that GParted doesn't change the start of the block while you are resizing the end!
I'm not sure why this happens but it might be the "round to sector" option. Double check before you hit OK.
I've had this happen twice now and it's seared painfully in my mind - it turns a 2 second operation into hours of data shifting and increases the risk of further problems. It'd be a serious pain to move back.
Never attempt to modify partitions without a proper backup, unless you're doing it to try to recover from a disaster that already happened where there is no backup. But then you'd do a copy of the entire disk first anyway ^^
To add some weight to this, I've lost data on partition resize with various utilities including GParted. It happens, even if it's supposedly rarely (yes I've had backups).