Whether you should register multiple domains really depends on the nature of the site you are building.
For example, hobbyists don't really need to have domains with the same name but different extensions; but for business it can be beneficial.
Domains ending in .COM have a high level of awareness in Australia and overseas; so it can be useful for an Australian business to register .COM.AU and also .COM; even if it's just to prevent a competitor or mischievous party from doing so. Depending on the party's intention, this practice is known as cybersquatting.
If you're selling goods to overseas people, particularly consumers or other businesses in the USA, also registering the .COM version of your name becomes an even better idea as out of habit USA users might type in the .COM name rather than .COM.AU.
It's a similar situation with .ORG.AU - registering the equivalent in .ORG is sometimes a wise move; particularly if an organisation has a presence overseas.
Beware: registering domains with various extensions can become a little addictive. With so many more extensions available these days (and more to come), it can become somewhat of an administrative nightmare managing a large number of domains - and rather damaging to the hip pocket. Just stick with the extensions that have the highest awareness in your target markets.
If you do decide to register a series of domains all with the same name left of the dot; remember to do something with them. Instead of them just resolving to an error page, perhaps point them at what is your primary site to help wayward visitors find your "real" web presence. This can be done with a 301 redirect.
When you have a number of domains pointing to the same site, keeping tabs on them becomes even more important as it can be easy to forget what is in your portfolio. Ensure you keep the contact details record of all your domains up to date. Failing to do so can result in one or more of your domains perhaps expiring without you realising it. Once expired, it may be scooped up by someone else.
How to register a name: Enter your choice in the search tool and click 'GO'. If after the check the domain names search results show your choice is available, you will then have the option to proceed to purchase registration; which is a very quick and easy process - start a search and find your ideal website address now.