A slightly different opinion here and one based on the fact I'm currently reading Fogg's Persuasive Technology about credibility of computers. The actually feature is a user set yes/no to writing a client-side cookie to reauthenticate future sessions.
But obviously you can't ask users "Do you want me to write a cookie?" ... however I'm wondering out loud if "Remember me?" is the best language. I would like to do some user testing with this, but what does that actually mean to people? Does the implied meaning properly communicate what the feature does and the security/privacy implications?
Thinking about the flip side, does not checking that box mean "I want you to forget about me". That approach may better define the function and consequences of the feature .. but how do people feel about asking an application to actually forget about them?
Sorry if I'm not explaining this properly - I'm just coming from the angle of perceived intelligence in technology and how a "forgetful" application could be seen as potentially untrustworthy as much as an application that you have to explicitly tell to remember who you are.