Would have to be Adventure World...it is exciting and heaps for all ages to do.
There is also a wonderful playground, though not in a park, at Coventrys, for younger children. It is not outdoors, however it is very safe and has foam on the ground and shoes are not allowed in the area.
There are so many good ones that its hard to know where to begin! Bayswater Riverside Gardens has a couple of great playgrounds (one which is fenced) and is right next to the river. It also has plenty of wide open spaces for organised games and paths for riding scooters and bikes.
Another popular one is Faulkner Park in Belmont, also known as the Volcano Park due to the big artificial volcano which is at its centre. Kids love this place and can happily spend hours here. It's also close to the Belmont Library, so you can retreat there when they tire themselves out.
John Oldham Park on Mounts Bay Road is also a magical oasis right in the heart of the city, while Heathcote Reserve in Applecross is awesome, with an absolutely massive adventure playground in the form of a pirate ship. Both of the places are definite winners with the kids.
Perth also has quite a few free water parks which are perfect for a hot day. Right in the heart of the city, Forrest Place has a water playground as does Hyde Park and Ellenbrook (Rainbow Waters). On Clarkson Road in Maylands, Maylands Waterland is also loads of fun although entrance fees do apply.