With openssl:

openssl x509 -enddate -noout -in file.pem

The output is on the form:

notAfter=Nov  3 22:23:50 2014 GMT

Also see MikeW's answer for how to easily check whether the certificate has expired or not, or whether it will within a certain time period, without having to parse the date above.

If you just want to know whether the certificate has expired (or will do so within the next N seconds), the -checkend <seconds> option to openssl x509 will tell you:

if openssl x509 -checkend 86400 -noout -in file.pem
then
  echo "Certificate is good for another day!"
else
  echo "Certificate has expired or will do so within 24 hours!"
  echo "(or is invalid/not found)"
fi

This saves having to do date/time comparisons yourself.

openssl will return an exit code of 0 (zero) if the certificate has not expired and will not do so for the next 86400 seconds, in the example above. If the certificate will have expired or has already done so - or some other error like an invalid/nonexistent file - the return code is 1.

(Of course, it assumes the time/date is set correctly)

Be aware that older versions of openssl have a bug which means if the time specified in checkend is too large, 0 will always be returned (https://github.com/openssl/openssl/issues/6180).

Here's my bash command line to list multiple certificates in order of their expiration, most recently expiring first.

for pem in /etc/ssl/certs/*.pem; do 
   printf '%s: %s\n' \
      "$(date --date="$(openssl x509 -enddate -noout -in "$pem"|cut -d= -f 2)" --iso-8601)" \
      "$pem"
done | sort

Sample output:

2015-12-16: /etc/ssl/certs/Staat_der_Nederlanden_Root_CA.pem
2016-03-22: /etc/ssl/certs/CA_Disig.pem
2016-08-14: /etc/ssl/certs/EBG_Elektronik_Sertifika_Hizmet_S.pem