How early should I apply for rolling admissions at state schools?

I'm interested in a few different state schools (UMass, Maryland, UConn, URI), and I noticed that many of them have rolling admissions. Should I try to apply as early as possible, or will it not make a difference? How early can I apply?

Technically, the earliest you can apply is August 1st (the date the Common App is released for your application year), but I wouldn't recommend rushing the process. In fact, the schools you've listed don't technically have rolling admissions except in some special cases for spring semester applicants. I've linked to their websites so you can see more details on the application deadlines. It's nice to get your college applications out of the way early, but you should give yourself a chance to retake standardized tests senior fall and come up with an awesome essay. These things will matter much more in the admissions process than when the school gets your application.