I think I can attempt to clear this up.
USB-100mA
USB by default will deliver 100mA of current (it is 500mW power because we know it is 5v, right?) to a device. This is the most you can pull from a USB hub that does not have its own power supply, as they never offer more than 4 ports and keep a greedy 100mA for themselves.
Some computers that are cheaply built will use an bus-powered hub(all of your USB connections share the same 500mA source and the electronics acting as a hub use that source also) internally to increase the number of USB ports and to save a small amount of money. This can be frustrating, but you can always be guaranteed 100mA.
USB-500mA
When a device is connected it goes through enumeration. This is not a trivial process and can be seen in detail on Jan Axelson's site. As you can see this is a long process, but a chip from a company like FTDI will handle the hard part for you. They discuss enumeration in one of their app notes.
Near the end of enumeration you setup device parameters. Very specifically the configuration descriptors. If you look on this website they will show you all of the different pieces that can be set. It shows that you can get right up to 500mA of power requested. This is what you can expect from a computer. You can get FTDI chips to handle this for you, which is nice, as you only have to treat the chip as a serial line.
USB-1.8A
This is where things get interesting. You can purchase a charger that does outlet to USB at the store. This is a USB charging port. your computer does not supply these, and your device must be able to recognize it.
First, to get the best information about USB, you sometimes have to bite the bullet and go to the people whom write the spec. I found great information about the USB charging spec here. The link on the page that is useful is the link for battery charging. This link seems to be tied to revision number, so I have linked both in case the revision is updated people can still access the information.
Now, what does this mean. if you open up the batt_charging PDF and jump to chapter three they go into charging ports. Specifically 3.2.1 explains how this is gone about. Now they keep it very technical, but the key point is simple. A USB charging port places a termination resistance between D+ and D-. I would like to copy out the chapter that explains it, but it is a secured PDF and I cannot copy it out without retyping it.
Summing it up
You may pull 100mA from a computer port. You may pull 500mA after enumeration and setting the correct configuration. Computers vary their enforcement, as many others have said, but most I have had experience with will try to stop you. If you violate this, you may also damage a poorly design computer (Davr is spot on there, this is poor practice). You may pull up to 1.8A from a charging port, but this is a rare case where the port tells you something. You have to check for this and when it is verified you may do it. This is the same as buying a wall adapter, but you get to use a USB cable and USB port.
Why use the charging spec? So that when my phone dies, my charger charges it quickly, but if I do not have my charger I may pull power from a computer, while using the same hardware port to communicate files and information with my computer.
Please let me know if there is anything I can add.
You cannot connect two USB ports in series to obtain a higher supply voltage. You will short out the PC's power supply and although USB is specified with protection for a similar situation, many motherboards do not implement that. This means you'll short the power supply and if you are lucky you PC will restart fine after removing the short circuit.
As an alternative look for a step up / buck / boost converter. These are available from many webshops/ebay for couple Dollars/Euro's and do exactly what you want: input voltage eg. 5V and output voltage most of the time adjustable.
Here is a random example of what I mean.
Best Answer
It might be possible in some cases, and it is probably safe to try.
USB only provides 500 mA maximum, and that is only after requesting and being granted that level of current. However, the spec does not say a port can't supply more, only the minimum it must supply in various circumstances. The extra logic to limit the port current only to what was negotiated isn't worth it on systems that have plenty of power availble. Consider that 500 mA at 5 V is only 2.5 W, which is small fraction of a 150-350 W power supply commonly found in desktop systems. On such systems, they usually just put a polyfuse in series with each USB power line and call it a day. If you don't draw more than 500 mA, all will be OK. Polyfuses don't have tight trip points, so there is usually considerable margin.
Laptops, on the other hand, have limited power and therefore do usually manage their USB ports carefully. There will always be some margin built in, but don't expect a lot more from a laptop USB port than what you're supposed to get. The margin will be just enough to guarantee the minimum is met under all conditions.
As for it being safe, probably most of the time. All these devices can't afford to blow up when something bad happens and power and ground are accidentally shorted at a port. I'd be surprised if you find a computer that is damaged by that. It's not that much more expensive to build in some basic protection, the probability of crap happening is high enough, and the cost of damage from it high enough that such protection is worthwhile.
Added:
There has been some comments that claim the USB spec requires a host to limit the current it sources to 5 unit loads (500 mA). That is not correct. It was also noted that some hosts blow physical fuses if devices draw too much current. That may be true of those devices, but then those aren't real USB ports.
From the USB 2.0 spec, section 7.2.1, first bullet, page 171, referring to hosts sourcing current:
... must supply at least five unit loads to each port.
Then in section 7.2.1.2.1 "Over-current protection" on page 173:
... The preset value cannot exceed 5.0 A and must be sufficiently above the maximum allowable port current such that transient currents (e.g., during power up or dynamic attach or reconfiguration) do not trip the over-current protector.
And later in the same paragraph:
The over-current limiting mechanism must be resettable without user mechanical intervention. Polymeric PTCs and solid-state switches are examples of methods, which can be used for over-current limiting.
So clearly: