Summertime in Sydney brings out all the "orb-weaving" spiders, which are prolific web-builders.
If you're the first person to walk down the footpath in the morning, you'd want to walk with your arm in front of your head or risk a face full of spider web (they like to string webs between trees, and it is quite a strong web - so even if you don't get the main part of the web, you'll most likely get one of the stronger supporting strands).
What's more - they repair their webs if they get broken, so even if you walk through one earlier in the day - you will possibly find something being reconstructed within hours.
Fortunately, these guys don't tend to come inside (in my experience), they just cover your yard in webs (if I look out my office window here at home, I can probably count about 50 webs strung from trees and bushes, and from our house across the yard).
We also get huntsmans at times too - these guys love to come inside and are quite active. The largest I've seen at home would have been wider than my hand-span, over 20cm wide I reckon ... but usually the ones around here are 10 - 15cm in leg-span. They don't tend to build webs - but they are prolific insect catchers, so are actually quite good to have around (if you can learn to live with them - which most people can't!!)
I try not to kill them, but gently use a broom to get them off the wall/ceiling and then take them out into the yard and relocate them. I did have one which took a particular dislike to that approach and ran up the broom handle - which is not a pleasant experience - he ended up dead from being uncooperative.
The white-tailed spider is well known and typically lives in garden areas. It has been known to cause nasty ulcerating wounds from its bite - so is best avoided. For this reason, it is not recommended to wander around in your garden in bare-feet and to wear gloves while gardening.
The black house spider likes to build messy webs around the outside of the house, particularly in the corner of windows - we have dozens of these along the southern (dark side) of our house - one day we'll get around to cleaning the windows and getting rid of them - they really are quite unsightly, but don't tend to bother us.
The Sydney Funnel-web is the most notorious of spiders in this area - has a bad reputation, and is known to be aggressive (or more accurately, to "look" aggressive - but they don't tend to chase people - it's just a defense mechanism!). However, they don't tend to come indoors, and it's only the males I think which are venomous (and they are one of the most toxic spiders around). I've never seen one - but then, I don't go looking for them, and the hospitals know exactly how to treat them (my wife was an emergency nurse at the largest hospital near-by and they are used to dealing with spider and snake bites).
Of course, then there is the famous Redback Spider. We had these everywhere in South Australia (where I'm from originally), and not quite so many here in Sydney. If you leave a piece of tin or corrugated iron lying on the ground (typically used for fencing in many parts of Australia), you'll inevitably end up with Redbacks nesting underneath it. The gas-meter box at one of my properties in Adelaide had a Redback nest in it. They are not uncommon in garden sheds or metal garages - anywhere warm and dry.
Redback spider venom is highly toxic - but effective antivenom exists, and death from bites is pretty much a thing of the past (generally, you'd have to be already weakened and unable to get assistance to die from it).
Redback's don't tend to come indoors, but a girl I know in Adelaide was bitten on the thigh by one when she put her jeans on - it crawled into them when they had been left on the floor. That's very unusual. She got quite sick but recovered fully (although mentally is still rather fragile when it comes to spiders - more so than normal, anyway).
Yes, we have a lot of spiders here - but you get used to them and learn to live with them.
More information about spiders in Sydney:
Wildlife of Sydney - Spiders - Arachnida