How do I verify or check cronjob is running or not under a CentOS / RHEL / Fedora Linux from a shell prompt?

cron or crond is daemon to execute scheduled commands (Vixie Cron) on a Linux or Unix-like systems. Usually, it is started automatically from /etc/init.d or systemd on entering multi-user runlevels.

RHEL/CentOS v4.x/5.x/6.x and Fedora Linux (older version) Verify Cron Service

You can simply use any one of the following command to see if crond is running or not, enter:
# pgrep crond
OR
# service crond status
Sample outputs:

crond (pid 4370) is running...

If it is not running type the following two command to start crond:
# chkconfig crond on
# service crond start
Verify cron is running by viewing log file, enter:
# tail -f /var/log/cron

A note about CentOS/RHEL v7.x+ and latest version of Fedora Linux

You need to use the following command to find out if the crond is running or not:
$ systemctl status crond.service
Sample outputs:

   Loaded: loaded (/usr/lib/systemd/system/crond.service; enabled)
   Active: active (running) since Tue 2015-05-19 14:53:32 EDT; 3min 7s ago
 Main PID: 1292 (crond)
   CGroup: /system.slice/crond.service
           └─1292 /usr/sbin/crond -n

If not running configure the crond service to start automatically on boot:
$ sudo systemctl enable crond.service
$ sudo systemctl start crond.service

A note about Debian / Ubuntu Linux (older version) Cron service

On a Debian and Ubuntu Linux cron logs its action logged to the syslog facility i.e. use /var/log/messages file:
# tail -f /var/log/messages
Find out if cron daemon is running or not, enter:
# pgrep cron
If not running start it, enter:
# update-rc.d cron defaults
# /etc/init.d/cron start

A note about Debian Linux v8.x+ and latest version of Ubuntu Linux

The syntax is as follows to check if the cron service is running or not:
# systemctl status cron
Sample outputs:

● cron.service - Regular background program processing daemon
   Loaded: loaded (/lib/systemd/system/cron.service; enabled)
   Active: active (running) since Tue 2015-05-19 11:49:32 IST; 12h ago
     Docs: man:cron(8)
 Main PID: 1053 (cron)
   CGroup: /system.slice/cron.service
           ├─1053 /usr/sbin/cron -f
           └─3020 /usr/bin/atop -a -w /var/log/atop/atop_20150520 600

If not running configure the crond service to start automatically on boot:
$ sudo systemctl enable cron.service
$ sudo systemctl start cron.service
See Debian / Linux service management for more information.