I've got a webapp running on tomcat utilizing a JndiRealm and form authentication. I must give a "remember me" checkbox to that particular form. What's the easiest method to do that?

That's pretty lots of work if you want to keep using container handled authentication because this facility is not supplied by the conventional Java EE API. Spring Security has done the majority of the meet your needs. Look into the Remember-Me Authentication documentation. I'd recommend it rather than homegrowing.