Penguins are a known attraction on Phillip Island. I know there are organised paying penguin sighting tours, such as the Penguin Parade. Is this the only way to see penguins on the island? Are there any do-it-yourself walks around the island from which one can see the penguins?
No, there aren't. While branded the "Penguin Parade", the entire penguin colony site is actually operated by Phillip Island Nature Parks, a non-profit organization, and the basic "General Viewing" option only buys you entry to the trails and seating area to watch the penguins waddle ashore. Actual guided tours cost more.
There are other penguin colonies in Victoria, but they're all some combination of inconveniently located and/or access restricted. The one exception that's both free and convenient to visit is the one right off St. Kilda, only a stone's throw from central Melbourne, but there are only a few dozen penguins living there with very limited viewing options, compared with the thousands easily seen from the purpose-built amphitheatres at Phillip Island. To be honest, given the selfie stick touting hordes they face every night, the real wonder of nature is why the penguins don't all bugger off to somewhere else...
There might be one way around paying for the entrance fee to the Penguin Parade. There is a public road (St Helens Road) overlooking the bay to which the penguins come at night, just above the actual Parade. One might actually be able to see the birds from there, if one brings a good pair of binoculars. Below is a screenshot of the map, whose detailed link is here:
The best way to do this would be to get there once the sun sets, so as to avoid being spotted by the Rangers, who might come and ask you to leave.
It is worthy to note that watching penguins from up there doesn't even begin to compare with seeing them close-up at the parade. IMHO it was money well spent.