Deciding whether you might be a ‘resident of Australia for tax purposes’ involves a careful consideration of your particular factual situation, in the context of a rather complex area of the law.

Australian tax law has statutory definitions of ‘resident’ for tax purposes. However, in the case of individuals the definitions use general terms such as ‘resides’ and ‘domicile’ and you need to look to the case law to help with that.

There are 4 basic tests for an individual: the common law based ‘resides’ test; the common law based ‘domicile’ test; the ‘183 days’ in Australia during the tax year test; and the public sector superannuation test. The ‘183 day’ and ‘domicile’ tests will not apply if the Tax Office is satisfied you have your usual place of abode outside Australia. The superannuation test generally only applies to certain public sector employees.

Depending upon your usual place of residence or citizenship, tax treaty provisions might complicate the issue and it is also possible to be ‘resident’ for tax purposes in more than one jurisdiction. You may also need to take the common law and statutory source of income rules into consideration.

Companies have separate rules not considered here.

The question of "residency" of Australia is a complex issue that needs to be decided on a case by case basis.
There are guidelines, as outlined in a previous answer to this question, but these are only precisely that, guidelines. There are also the Double Tax Agreements between jurisdictions to consider. Seek professional advice on this matter with more precise detail.

SOUTH AFRICAN Perspective: I agree with the answers below yet wish to highlight a unique South African perspective, in that the Aus/RSA treaty has no reference to habitual abode and specifically excludes from the treaty definition ATO tax residents paying Australian taxes on source only. In terms of a 2006 amendment, albeit that you are tax resident per any of the tests below, until PR is granted it may be acceptable NOT to include SA or worldwide income in the ATO return. Accordingly the Mel James comment on treaty rules are extremely critical! Back to the habitual abode, it is therefore often the case that expat South Africans living in Australia remains to be tax non-resident in Australia due to the nationality test following the centre of vital interest tie breaker which could not provide an answer. The exchange control rules in SA often denies the right the extract funds / wealth from SA leaving the centre of vital interest back in SA.