Is a visa required, or is just a passport enough, for a short holiday trip to Australia?
Specifically, how is it for citizens of Nordic EU member countries such as Finland?
Yes, a visa is required for EU citizens.
Fortunately, getting one is free and (usually) pretty quick. The easiest way is to apply for eVisitor online. See "Eligible passport holders" on that page to check if you are eligible for eVisitor.
The eVisitor allows visitors to travel to Australia for short term business or tourism purposes for up to three months. eVisitor applications are free and are available to passport holders from the European Union and a number of other European countries.
More information on Australian visas can be found at https://www.homeaffairs.gov.au/trav/visi
Many visitors to Australia like to stay longer than the 90 days you get on the free eVisitor visa.
In that case you need an Tourist Visa (Subclass 676), which allows you to stay six or even twelve months. This visa is not free, more information can be found at www.immi.gov.au/visitors/tourist/676/
Please note that after applying for a visa you need to use it within a year. I never made it to Australia in the first 12 months of my trip and had to buy another visa when I finally got there.
Actually... ALL citizens, except New Zealand citizens need a visa to enter Australia. As other people have suggested above, only European and a few other countries can apply online, which is quick. Visitors from most other countries are ineligible to do it online and must wait days for a paper based application process to be complete.
So, although you need a visa, it is a quick, online one... and issued free of charge :)