Well, that comes down to what people consider "fair use". Although not worded that way, the Copyright Act includes some provisions under certain circumstances where it would not be considered an act of infringement. Some examples being (there are many others):
For literary, dramatic and musical works:
Section 45 - Reading or recitation in public or for a broadcast
For computer software:
Section 47B - Reproduction for normal use or study of computer programs
Section 47C - Back-up copy of computer programs
Section 47D - Reproducing computer programs to make interoperable products
Section 47E - Reproducing computer programs to correct errors
Section 47F - Reproducing computer programs for security testing
For artistic works:
Section 47J - Reproducing photograph in different format for private use
Other works:
Section 40 - Fair dealing for purpose of research or study
Section 41 - Fair dealing for purpose of criticism or review
Section 41A - Fair dealing for purpose of parody or satire
Section 42 - Fair dealing for purpose of reporting news
Section 43C - Reproducing works in books, newspapers and periodical publications in different form for private use
The act also allows you to "format shift" items you own such as books, photographs, audio CDs and films on videotape (but not DVD/Bluray). For example, you can copy an audio CD you own into another format (such as MP3, FLAC etc...) for use inside or outside domestic premises (for example, your own car) but only for private and domestic purposes and for use by the owner of the item and members of their household. Under the act, you are only permitted to make one additional copy and that copy must be in a format that is different to the original. You obviously can't sell or distribute the copy and if you cease to own the original, the copy must be disposed of (otherwise it will be considered an "infringing copy").
Interestingly, the act also allows you to circumvent "copy control technological protection measures" (but not access control technological protection measures) and it is also lawful to circumvent region coding mechanisms on DVD as it's not considered an "access control TPM".
Also, people seem to confuse "making infringing copies" with "downloading". In Australia, there is no law against merely downloading or possessing infringing copies (provided you didn't make the infringing copy). Not that I condone torrenting etc... but as long as you don't upload, you aren't breaching the copyright act (at least, for now).
Sources:
http://www.austlii.edu.au/au/legis/cth/consol_act/ca1968133/http://www.copyright.org.au/acc_prod/AsiCommon/Controls/BSA/Downloader.aspx?iDocumentStorageKey=aa2b1da4-ae92-4e86-adcc-ffeb1c36bed6&iFileTypeCode=PDF&iFileName=Copying%20and%20Converting%20Formats%20for%20Private%20Use