Best & Simplest Application (Paid or Free) for Creating Hard Drive .dmg for Backup?

I'd suggest looking at CarbonCopyCloner. It works rather well for what you want.

[[ My goal is to find a program that will easily create a complete disk image (.dmg) of my laptop's hard drive which I can offload to an external drive for backup purposes. ]]

Hmmm.
This doesn't make sense.

You won't be able to boot from a disk image in a "moment of extreme need", such as an "I can't boot" situation.
You won't even be able to mount it, if your MacBook won't boot first.

If you want a quick, easy, and readlly-accessible backup on an external drive, your best bet would be to create a bootable clone external drive using either CarbonCopyCloner or SuperDuper.

You can then connect the cloned backup and boot your MacBook from it -- VERY useful to have for such moments of need, as above.

I suggest you do this:

- If you don't yet have an external drive, get one
- Download CCC from here:
http://www.bombich.com/download.html
(Free to download and use for 30 days)
- Create the cloned backup (very, VERY easy)
- Do a test boot from the backup by restarting and holding down the option key until the startup manager appears. Then select the backup and hit return.
- Done!

Bootable backups are definitely superior, assuming you are not looking for some kind of hardcore encryption. I used SuperDuper! for years, but have since made the switch to Carbon Copy Cloner.

There's a nifty little program that allows booting from a disk image on an Intell Mac. I don't recall the name of it, but I've used it in the last with great results.