You learn something new every day! Today I learned about the disown builtin in bash and zsh. When you disown a job, it will no longer receive a HUP signal when you exit your shell.

catlee@sherwood:~ [1015]% while true; do date >> date.log; sleep 10; done&

[1] 7380

So now you've got the current date being appended to date.log every 10 seconds. Try exiting your shell:

catlee@sherwood:~ [1016%1]% exit

zsh: you have running jobs.

But use the disown command:

catlee@sherwood:~ [1017%1]% disown %1

catlee@sherwood:~ [1018]% exit

and your shell exits without complaining. Meanwhile, your job keeps running in the background!