If someone in your family tree moved to Australia, or even if they simply visited, there may be an online record of their journey in the Index to Passenger Arrivals at the National Archives of Australia. From the main page of the Archives, click on Record Search (in the upper right hand corner of their website), then Search Now as a Guest, and finally, Passenger Index (again, upper right), to conduct a search.
The Index, which includes almost a million names, covers arrivals in Australis by ship between 1921 and 1950, and arrivals by air between 1944 and 1950. These include immigrants, business trips, tourists, and so on. You can search on first names with or without last names, and narrow down your searches by date, ship or aircraft names, or points of embarkation and disembarkation.
The Australian Archives site also offers a Photo Search, and specific Name Search tool, and a generalized search of the entire website, all of which can be useful in exploring your family connections to the land down under.
Grandma in Australia? National Archives of Australia, Image 11697818
You may not be aware of any connection that your family history has to Australia, but that doesn't mean the connection doesn't exist. The National Archives site is certainly worth a quick search, to see what turns up.
Visit the main page of Free Genealogy Tools for more, umm, free genealogical tools.
And don't forget to also check for your family history at NewspaperArchive.com and Ancestry.com.
These are subscription databases, but they are among the most powerful research tools available for looking into family roots.