Both are correct, but there is a slight difference in them.
Things changed--the event is in the past.
Example: We weren't getting along, and then suddenly, things changed. She started to do nice things for me, and I could not help but return the good deeds.
Things have changed--implies a recent event whose effects are still being felt, denotes a current situation or condition.
Example: When I was growing up, you could leave the door unlocked. Things have changed--I now have four locks on my door and carry mace.
There is some flexibility between the two, but that's it in a nutshell. Hope this is clear.
Z.
