It depends on the exact level of risk that you want, but if you want to keep your risk close to zero you're pretty much stuck with the banks (and those rates don't look to be going up any time soon).
If you're willing to accept a little more risk, you can invest in some index tracking ETFs instead, with the main providers in Australia being Vanguard, Street State and Betashares. A useful tool for for an overview of the Australian ETF market is offered by StockSpot.
The index funds reduce your level of risk by investing in an index of the market, e.g. the S&P 200 tracked by STW. If the market as a whole rises, then your investment will too, even though within that index individual companies will rise and fall.
This limits your potential rate of return as well, and is still significantly more risky than leaving your cash in an Aussie bank (after all, the whole market can fall), but it might strike the right balance for you.
If you're getting started, HSBC, Nabtrade, Commsec and Westpac were all offering a couple of months of free trades up to a certain value. Once the free trades are done, you'll do better to move to another broker (you can migrate your shares to the others to take advantage of their free trades too) or to a cheaper broker like CMC Markets.