Yes, I would always recommend having at least a matching pair eg. “com.au” and “.com”
The reason being your domain name is your online identity, it should be the portal to your business and your business alone. Too often I have seen clients purchase only one domain name to save a little bit of money per year, but have soon found a competitor or even an ad website spring up on the domain name they passed up on.
This is the reason why we provide 2 domain's with all our Sitebuilder Subscriptions.
Why would someone buy another version of my domain name?
The simple answer is to siphon traffic from your success, think how simple it would be for someone not to type the .au at the end of your domain name? How would you feel if they were to type what they thought was your domain name and find ads for Viagra instead? Having another site with an almost exact name also waters down your search engine results.
It’s simply not worth the risk
Domain names are so cheap per year that you might as well protect yourself by getting multiple domains.
Should i register more than a matching pair eg. “com.au” and “.com”?
This is completely up to you, a "com.au" and ".com" domain should be fine because in Australia these are the two most common domain name extensions. However If you are an organisation i would recommend ".org.au" and ".org" matching pairs as well.
Once you have purchased all your domain names, you can make one domain your Primary.
This is where you will setup your website and email hosting.
All other domain variants can be redirected to your Primary and don’t need hosting of their own, this ensures that google knows not to index all the other domains, so your primary is the only one that shows up in results and it also ensures that nobody can siphon traffic from your site with ad’s or redirecting to a competitors site.