Sounds like this question has mixed results. The de facto standard is to treat local mailboxes as case insensitive, but the official standard says case matters (though even the official standard mentions the de facto standard).
As other people have pointed out, it is possible that [email protected] and [email protected] are two different people, and both of them want to use your site. But on the other hand, it is far more likely that [email protected] and [email protected] are in fact the same person. If they type it one way one time, and another way another time, you probably want to let them in either way.
I'd suggest keeping track of both. Since using case insensitivity is so widespread, take their sign up email address and make it lower case. Whenever they try to log in, convert that to lowercase as well, for comparison purposes, when you go to see if the user exists. As far as sign up and sign in go, do a case insensitive comparison. If the person signs up as [email protected], you'll still want to allow them to sign in later with [email protected] or [email protected].
But you should also keep track of the email address that they signed up with in a case sensitive fashion. Any time you send an email to them, be sure to send it with that original casing. This allows the email server to handle it however it feels like it needs to. So even though the person may always be signing in to your site with [email protected], if they signed up as [email protected], you'll always send email to [email protected], just to be safe.
Some day, the de facto standard and the official standard will hopefully be the same. It's too bad we have to deal with this issue at all.
A couple of related side notes. The domain name (after the '@' sign) is always considered case insensitive, so you can always treat that in the same way. Second, just as important as the case sensitivity issue, you want to also be sure your site accepts all legal email addresses, which includes allowing all symbols that are allowed in email addresses. It is really frustrating for users who enter their legal email address, only to have the system say "the character '!' is not allowed." The standard defines what is allowed, but Wikipedia also has a good summary of this.