Modules
For Arduino, Raspberry Pi and other types of modules, Little Bird Electronics has the largest range in Australia. They are a reseller of the major hobby electronics suppliers such as sparkfun, adafruit and pololu.

Also Freetronics is a good little Australian company selling arduino compatible boards and modules.

Australian Robotics has a similar but smaller range than Little Bird. It is worth a look though because they often have some different types of motors and hardware which might suit your project better.

Ocean Controls sells more industrial stuff. Much more expensive, but it's where you want to look if you're thinking of a big project like building a CNC machine.

Components
In a rush go down to Altronics. The selection is ok (not much surface mount stuff) and generally expensive, but it will get your project finished in a hurry. Don't order from them, there are other much better online options. There is also Jaycar. The have a similar store but I usually avoid going there because the staff look like used car salesmen and come out the back room stinking of cigarettes.

Element14 has a much larger range and generally is the first place I look. Search and navigation is good, although the stock and expected delivery times don't seem to be very reliable. Good for larger quantities and when you can wait a few days for delivery.

Digikey and Mouser also provide the same service as element 14. If you are relly being fussy with your specs it is a good idea to check all 3 and see who has to best match for you. I was always worried about delivery from US being slow but they are usually very fast.

RSComponents is not as good at the others for sourcing components in my opinion, but they have the best range of chemicals, tools and consumables. I usually buy those kind of items from here.

PCB Manufacture There is a limit to how fine you can make a PCB in the garage, and when I need to outsource I use PCBCart. They are very easy to submit designs to, they can work with eagle board files, and have a different pricing scheme for small runs (5-20 boards) and larger orders in the hundreds. They have always met their quoted turnaround time and DHL shipping comes in a few days (although a bit expensive). Their support is very quick to respond via email, and their English is excellent so communication is no problem.

The following are walk-in store in the Melbourne eastern suburb area. I don't know of any mail order timber sellers.

Matthews Timber has a large range of specialty hardwoods and is very hobbyist friendly. Just walk through the office to the main warehouse and you will find a big wall with many racks holding several dozen species of timber. Boards range from an inch thick up to 3 inches. A lot of boards are rough sawn only, so you will need to dress them yourself. They will cut the board up for you in whatever size pieces you need to fit it in your car.
It is not cheap though. As an estimate, a 25mmx200mm board will start from around $25 a metre for local wood, up as much as $40 per meter for the more exotic imports like Zebrno.

Carbatec also has a small range of timber in it's store. It is much more expensive but comes in smaller pieces. You can also find things like pen turning blanks and sheets of veneer, so if you have a small project in mind and only want to buy what you need then it is worth a look. Very good and knowledgeable staff who are happy to talk shit about woodworking all day if given the chance.

A&E Metal Merchants online sells gold, silver and a few other base metals in sheets, granules, stamped blanks and a few other shapes. Also precious metal findings and tools sold. Prices are roughly tied to market value of the metal. I've ordered online a number of times and never had any issue.

There are a few online suppliers of jewellery making accessories out there, but I have found the best site to navigate, and the best service from Over The Rainbow. Has a larger range of cheaper alloy metals than A&E, plus a massive range of findings and good quality tools for pretty much any type of jewllery crafting. I highly recommend this store for any jewellery making supplies.

The following are walk in stores in the Melbourne eastern suburbs area. Although some provide shipping it is generally by courier and a bit expensive for a hobbyist to justify.

Aluminium
Aluminium Trade Centre has all sorts of shapes. If you walk in off the street they have racks in their reception area and you can see samples of all the shapes on offer if you need to take a closer look first. All prices are available online and can be cut to size. I find it easier to place an order online with all the cut lengths I want, then pick up when ready. An order placed before noon is usually ready to pick up later the same day.
Be aware thought that their stock is structural aluminium and is not the best for machining (thought they do have some 2011 alloy in 50mm round bar).

Brass Copper
George White & Co has a large supply of brass and copper. Walk in off the street and someone will serve you at reception. You can see what the range is online but there are no prices ($18-$20 per kg will give you s rough estimate). Generally only the brass and copper is what they have ready to cut for you, if you want any of the other metals on their website it would be best to call first. They do stock a small variety of 2011 aluminium, but stock varies so you will need to ask what they have on hand.

Steel
While you should be able to find most of what you want at Bunnings, if you have special needs or just want someone to cut it up for you use Online Steel Suppliers. They have a few places around Melbourne so you should find one not far away. They don't have much in the way of a proper shopfront (in Springvale anyway), so place order online and pick up when they give you a call.

Everywhere should have a few local places around to find some good stuff, but for specialty items you need to look online. Especially for smaller screws and stuff.

Bolts & Industrial Supplies has a very extensive range. If you need a screw or bolt just the perfect size this is a good place to look. Cheap prices for buying in lots of 100. I've had good service from them.

Small Parts and Bearings has lots of tiny and obscure fasteners among other things. Also one of the few places you can short lengths of music wire for making springs.The website looks like its from the 90s and is crap to navigate, but the checkout does work smooth and service is timely. Item prices can range from expensive to completely absurd, but if you are going to have a hard time finding it elsewhere it may be worth it.

Not so much use for hobby work, but for the motorbike Pro-Bolt has a great range of engine and fairing bolts. Sorted by bike model you can get all sorts of fancy coloured bolts and other fittings. If you are doing a respray job you can find fasteners here to finish it off nicely.

This one is a pain in the arse thanks to the nanny state. But there are still a few options out there if you look hard. I would be very appreciative of any other tips on where to get chemicals.

Hydrochloric Acid
Sometimes called muriatic acid in other peoples guides, this is something you can still get at Bunnings. It will be behind the trade desk so go there to ask.

Ferric Chloride
For etching copper, brass and alloys. Best supplier for this is RS components. Jaycar and Altronics only have Ammonium Persulphate which requires a higher temperature to work properly, so I prefer Ferric Chloride.

Ferric Nitrate
For etching silver. Anpros has this and sell it to the public. I went out to Bayswater to pick it up, but they claim they will ship it. They appear to cater mostly to winemakers, so may have a few other chems you need.

Sulfuric Acid
Would be great for anodising aluminium. Still have no idea how to get it. Apparently the feral rat-faced guy at batteryworld cant sell it to a guy with a PhD in physics. The government seems to think Dr Steve is the one who is most likely to use it for synthesising drugs, and batteryworld man is upholding the moral fabric of society. I feel so much safer already.

Big Tools
Hare and Forbes has a good range of larger machines and tools for metal and wood working. They usually have a small version of each type of tool on sale at an affordable price.

Wood Tools
Carbatec has a great range of top quality woodworking tools. Hand tools, machines and joining jigs. There online delivery is pretty good, but it is better to visit the store if you have one near.

Mini Mill/Lathe Tools
Ausee has a good range of tools and accessories for mini engineering. Shipping quick.

LPR Toolmakers is also good for finding engineering tools. Purchased from them before, never had any trouble.

CTC Tools has a lot of cheap cutters and things like that. Shipping can be expensive and may take a week or two, but if you fill a cart you can make some good savings overall.

McJing has an online store and shopfront in the outer Sydney area. I haven't used them, but a very reliable friend recommends them highly, especially if you can visit the store. As well as the tools advertised on the website their shop apparently has a decent stock of small lengths of various metal and plastics.

If you can't find the mini lathe/mill accessory you want at one of the Australian stores, then ArcEuroTrade has it. Shipping from England is not too bad, usually only about a week. I've upgraded a few machines thanks to this store. Anyone with one of the seig brand mini machines will become very familiar with this store.

Hobby Tools
My Tool Store has a lot of hobby size tools and accessories. I've purchased from here a number of times with no trouble.