The obvious free option is Time Machine. If you want to go this route, then you might want to look at this article: http://www.macworld.com/article/1131841/multiplebackup.html
Note that Time Machine will backup EVERYTHING unless you tell it to specifically exclude certain items. You will want to consider one of the first two options in that article.
The next option is to "manually" do it. This basically means you connect the drive and them manually copy over the items you want to backup just as you would otherwise copy/move files normally. This option becomes very tedious if you have a large number of different items to backup.
So, then the third overall option is to use some sort third party backup software. Carbon Copy Cloner is one example. There are many others. Which one you choose will depend on what you want to achieve (i.e. a clone, an incremental backup, or "syncing" particular files, etc), how much you want to pay, etc.
In my case, I use SuperDuper! (nominally a competitor to Carbon Copy Cloner) as my primary backup. Then use Time Machine as a secondary backup. And lastly I use a manual copy of some files as a backup "archive" (good example is my iTunes library...while the overall library might change, the specific individual media files generally will not).
FWIW, the SuperDuper license does allow you to use it on multiple Macs to my knowledge. This appears to be the same for Carbon Copy Cloner (see the last item): http://help.bombich.com/kb/overview/carbon-copy-cloners-transition-to-a-commercial-product-frequently-asked-questions