How can I unseal a bottle of glue that has been sealed shut?
PVA glue doesn't bond well with the plastic the bottle is made of; the dried glue peels off easily if you start at one spot.  It's harder to separate the glue and get the cap off when you're working against a lot of glue surface area at once.
If you grab the base of the cap with pliers, you can typically get enough leverage to break the glue bond and unscrew the cap without damaging anything.  Once it's open, you can peel the glue out of the dispenser tip and get any dried glue out of the bottle neck.
If brute force isn't enough to unscrew the cap, you can warm it to soften the glue a little, as Joachim suggests.  That will help it stretch and peel as you unscrew the cap.
Actually, depending on the glue, freezing it to make the dried glue harder can also sometimes help if the bottle is empty and you just want to save the bottle for reuse.  It makes the glue less flexible, so brute force can more easily break the bond.  But freezing can ruin any remaining good glue, which is your goal, so this wouldn't be applicable in this case.