I have a Verizon iPhone 5c. Is it unlocked so that I can just go to T-Mobile or AT&T prepaid, by just popping in the SIM card?
If you bought the iPhone at full price ($549 or $649) then yes it is unlocked.
If you and bought it subsidised (where the price is $99 or $199), no it is not.
This restriction is required by the carrier, because they paid the remainder of the price, and will claim it back from you (with a tasty profit!) over the duration of your contract with them.
First things first: if you have inserted a Verizon SIM card (or any other carrier's SIM card) within 20 minutes of turning on your iPhone, you are out of luck as it will ONLY work on that carrier. This is a very weird thing that happens with the iPhone, but I believe Apple added this on purpose to sidestep something within the carriers.
As for whether or not a prepaid plan will work, apparently it can. There is a webpage on WikiHow that explains how to do it (look at the iPhone 5 method in your case).
I'm not too sure if it will work on a Verizon iPhone, but it never hurts to try.