For regions with lots of rain, crowded plants are likely to get various sorts of infections.

If you tell us where you live, perhaps other folks from that area might suggest what's occurring.

Or take samples and good images to your county's Extension Service office where folks will look at the first-hand.

To find your county's office --

http://npic.orst.edu/pest/countyext.htm

Thanks for responding Jean! I did more research after posting this, and I'm pretty sure it's early blight. We planted them way too close & didn't rotate them. This is our 2nd year doing a garden & we are learning a lot! Maybe someday we'll have it perfected! :-)