I have some friends who are PR of Australia and I wonder what countries allows Australian permanent residents to visit without a visa? I know that New Zealand doesn't require a visa for Australian permanent residents, but are there any other countries? Also does being an Australian Permanent resident give any advantages when applying for any visa? Like what are the travelling benefits an Australian Permanent resident has?
Most visitor visa regimes are based solely on citizenship, with permanent resident status having no effect. There are some exceptions, however, where countries that have unusually close relationships will waive visa requirements for one another's permanent residents. The exceptions I know of concern certain cases in the EU, and US permanent residents, who do not need visas for short visits to Canada. I was unaware of a similar arrangement between Australia and New Zealand, but I am not surprised to learn about it.
I don't know of any other countries that exempt Australian permanent residents from a visitor visa requirement.
Transit visas are another matter. Many countries will waive transit visa requirements for those with permanent resident status in certain "developed" countries, such as Australia. The UK comes to mind, as does South Korea (thanks to jpatokal for pointing that out).
Singapore and Philippines waive visa (Tourist/Visit) requirements for Aussie PRs regardless of their passport.
Visa is available in Singapore only for Air Travel (Entering from Malaysia by road doesn't entitle a visa-free entry)
For Philippines, visa free entry is available only at Manila airport.
Some of the information contained in this post requires additional references. Please edit to add citations to reliable sources that support the assertions made here. Unsourced material may be disputed or deleted.