If you haven't, then now is the time to have the talk. Let him know that although you feel close to him and don't mind sharing a bed, you don't want to share email addresses, and politely (and even humorously) tell him to butt out of your accounts. If this is the first offense, I wouldn't make it a big deal but if the behavior continues, you may have a bona fide snooper on your hands.
To see how I'd handle an online busybody, just
If this is a reoccurring event for your online peeping Tom, then you need to be firm and direct. Snooping in your email and online networks is just as bad as opening your snail mail — although it's not a federal offense, it's just as intrusive. But trust could be the root of the problem here. If your BF doesn't trust you, it's likely that email correspondence would be the first place to find out if you've been naughty or nice. Find out why he's snooping around your online life, and you'll have an easier time figuring out how to remedy the problem.
If you have no reason to be considered untrustworthy, this could end up being a losing battle, especially if your partner has a history of being the victim of infidelity. Talk it out, and if you can't come to a common ground, then it may be time for you to weigh the pros and cons of living with a snoop.