I have written a Python script that checks a certain e-mail address and passes new e-mails to an external program.  How can I get this script to execute 24/7, such as turning it into daemon or service in Linux.  Would I also need a loop that never ends in the program, or can it be done by just having the code re executed multiple times?
If you are using terminal(ssh or something) and you want to keep a long-time script working after you log out from the terminal, you can try this:
screen
apt-get install screen
create a virtual terminal inside( namely abc): screen -dmS abc
now we connect to abc: screen -r abc
So, now we can run python script: python keep_sending_mails.py
from now on, you can directly close your terminal, however, the python script will keep running rather than being shut down

Since this keep_sending_mails.py's PID is a child process of the virtual screen rather than the
  terminal(ssh)

If you want to go back check your script running status, you can use screen -r abc again
How to make a Python script run like a service or daemon in Linux