score:10
You have to be able to justify the purpose and conditions of your visit (Schengen Borders Code 6(1)(c)). Unlike a visa applicant, however, who is required to submit documents supporting this justification in applying for a visa, the chance of your being asked for documents is exceedingly low.
Tourists sometimes -- or perhaps even usually -- plan their visits independently without having anyone to invite them. In such cases an invitation letter isn't possible except to the extent that a hotel could issue one, but instead of requiring that, Schengen authorities are happy to see proof of a reservation.
A visa applicant who is staying with a friend or acquaintance will want to include a letter from that person acknowledging this fact, in order to satisfy the visa officer that accommodations have been arranged. Border officers, in the other hand, don't often look at the accommodation arrangements in detail. If you are visiting someone, you won't need a letter. In the unlikely event that immigration officers are skeptical, you might invite them to call your host on the phone.
In terms of both accommodation and departure from the Schengen area (where people sometimes erroneously think that an onward ticket is required for entry) all you need is to show credibly that you can arrange it. In other words, you need money or a credit card. Even there, you won't likely be asked to show that you have them unless perhaps you're particularly young. Dress well, look affluent, and you're unlikely to receive much scrutiny.
It's unfortunate that these decisions may be influenced by the traveler's personal appearance, but it's nonetheless the case. If you look non-European then you may want to pay a little more attention to having documentation available in case you're asked for it. But don't volunteer anything other than your passport, lest you appear overeager, which can also arouse suspicion.
Upvote:7
No, Australian citizens do not need a letter of invitation to visit a Schengen country.
Furthermore, as noted by the Australian government, "Australians don't need a visa to travel to countries in the Schengen Area for up to 90 days in any 180-day period... [for] tourism and holidays." The linked government FAQ covers the practical requirements.