In Melbourne it is free to take your bike on a suburban train at all times. This is a great way of extending your travel range with little cost.
When taking a bicycle on the train it's important to be considerate of other passengers. If at all possible travel outside of peak times as the trains can get a little crowded. Preferrably travel at the rear of the train where there is more space to store your bicycle, do not use the front of the train as people with disabilites may need to use that section.
Be mindful of your bicycle at all times. It's your responsibility to ensure that your bicycle does not interfere with other passengers.
Virtually all ferries accomdate the transport of bicycles, however there may be a nominal charge so check with the ferry line first to avoid nasty surprises.
Be prepared to use some padding, bungees and a little ingenuity to secure your bike for the crossing. While there's a lot of room on a car deck there's rarely any bicycle specific fixtures so you'll have to secure your bike as safely as you can for the crossing.
It's not widely known that air transportation of bicycles is free within Australia. You'll have to take care of packing your bicycle yourself and there are several soft and hard cases on the market which makes this task easier.
It's wise to check in a little earlier than normal to allow baggage handlers time to help and advise you on the packing and carraige of your bicycle, especially the first time you do it. Don't be afraid to ask the advice of your local bike shop. Anyone care to write a guide for transporting bikes by air?
International travel with a bicycle is not guaranteed to be free; many airlines give you an extra baggage allowance, some count it towards your normal baggage allowance and some others may charge. If you're considering international travel with your bicycle it's worth asking; the cheaper airline may not be so cheap if it carries punitive costs for carrying bicycles.
OK, you really want to minimize your impact on the environment but there's just no public transport which gets you within a reasonable distance of your destination. It happens, especially in a country the size of Australia which has many sparsely populated regions.
There's nothing for it, you've just got to get in a car. At least for some of the way. Often we get to a destination and the bulk of the mileage is getting to that destination. If you're going to spend an amount of time at your destination, bringing your bicycle along is a good thing to do. Riding around a town is a great way of getting to know the area and it's so convenient as well. When riding a bike stopping to check something out is easy, you can stop anywhere because as soon as you get off the bike and walk you're a pedestrian.
Next time you're on the road, think about taking your bike. It may well open a whole new side of your destination to you.
Multiple bikes and Foldable bikes
In locations / countries where bringing your standard bike is not free, or not possible, it may well be possible to park an inexpensive bike well secured at a station or similar, and use another on at the other end. This is quite common in Denmark and the Netherlands. Another option is to purchase and bring along a foldable bike. Three well known brands are Brompton, Birdy and Dahon. Such bikes are enjoying increasing popularity in the Netherlands, the UK and elsewhere.