There are several reasons for this,
Reason 1: The email may be sent to your inbox and it may be trapped in the spam box. Check the spam box to ensure your email is not their in the spam box. Gmail using a complicated algorithm to classify emails to spams and send the spam emial directly to the spambox. So it never appears on your inbox. To show it in your inbox, visit spambox find the email that you want to move to inbox and do move the email to the inbox.
Reason 2: The email may not be delivered to your inbox, due to queue or slow processing of email request by some scripts. I noticed this type of problem in several websites, which need a verification number from the inbox to complete the registration process of site/application. Several times I received such emails after a long waiting. For this case you need to wait and want to check the mail after some time.
Reason 3: Check the email address. If there is any error in the email address while typing the email ID may cause problems. The email may send to a wrong address !
If all this failed and cannot find/retrieve your email, then after verifying the accuracy of the email ID,ask him/her or click resend email button/link (if it is a program) to re-send the email !