Click on Settings (under your name on the right side of the page)
Click on Email Settings (left side of page, under Profile)
You will now be able to change the following options:
The types of messages you're willing to receive
The frequency of emails
Who can send you invitations
The frequency of group digest emails
Click on each option to change your settings. For example, if you click on "Select the types of messages you're willing to receive" you can choose Introductions and InMail or Introductions only. You can also uncheck the boxes next to the types of Opportunities listed if you don't want to receive them.
In the "Set the frequency of emails" section you can choose individual emails, a daily digest of all your messages, or no email. You can also select who can send you invitations, how much email you get from the groups you belong to, and what communications you want to receive from LinkedIn.
If you select individual emails you'll get a separate message for every notification on LinkedIn. The daily digest option sends a once a day email that includes all your messages, and no email means that you won't get any mail from LinkedIn.
You can quickly edit your settings to reduce the volume of email you get from LinkedIn to a manageable amount. Even if you do turn off most email messages you'll still be able to view them in your In Box, which has sections for Invitations and Messages from other LinkedIn users.
How to Use LinkedIn: