Are you using the web-interface at https://mail.google.com/ to access your account, or an e-mail client or mobile device?

Have you looked in the All Mail label for the missing messages?  What about Trash?  What about Spam?

Have you used the Search Mail function at the top of the page to look for the missing messages?

Do you have Settings->Inbox->Inbox Type set to anything other than the "Classic" view?

Look in Settings->Filters and Settings->Forwarding.  Is there anything defined?

Do you access your account with an e-mail client (Outlook, Thunderbird, Pocomail, etc), phone, notifier, or any other add-on/tool/web-site/etc?  Is anything enabled in Settings->POP/IMAP?

Check Settings -> Accounts and Import -> Change Account Settings -> Other Google account settings -> Authorizing applications & sites.  Have you given account access to any other web-sites or utilities?