Noctuid moth larva, cutworm or armyworm of some kind. Pick them off or use BT products or other control.

These turn into brownish medium-size moths that you likely see around your property.

To find out which moth it is, rear the caterpillar in a clear container with a "breathable" lid -- perhaps a piece of window screen held in place with a rubber band.

Feed it broccoli leaves.
Clean the container as needed. (Cats product lots of poop.)
When it pupates, wait until the moth adult emerges, then post its picture in this thread.

I have been picking them off like crazy. If I can find something to keep it in I'll try that. My daughter will LOVE that.

It's called the Cross-Striped Cabbageworm, Evergestis rimosalis.

In that case it is a crambid, and not a noctuid. Different moth families.

A beautiful caterpillar.