Are plastic fizzy-drink bottles an acceptable substitute for glass bottles?

You can certainly use plastic bottles like this. In fact, one introductory homebrew kit, Mr. Beer, includes these types of bottles.

One main advantage is that you can give the bottles a squeeze to gauge the carbonation level. When the bottles are hard, they are ready for consumption.

Keep in mind that lighter color bottles (plastic or glass) will allow more UV light to enter the beer, which can give it that 'skunky' aroma. If you can find them, use brown plastic bottles. (I have never seen any of these, except for the Mr. Beer ones, so you may have trouble finding them.) Otherwise, be sure to keep the bottles shielded from light.

Also, the same concerns that apply in the plastic vs. glass debate for fermenters apply here. Plastic can scratch more easily, and when it does, it can be very hard to sanitize effectively, since bacteria can hide in the scratches. On the other hand, if you drop a plastic bottle on your concrete patio, there won't be any broken glass!

If you're serious about your brewing, I'd recommend you don't use PET bottles at all:

1. Commercial soda bottles are thin walled, and will deteriorate over time in sunlight, or with any sort of heat treatment, whereas glass bottles can be washed in your dishwasher.
2. Clear colored PET will allow your beer to suffer from "light-strike", producing unsavory flavors and aromas to develop in your beers, even if you are careful about keeping your bottles in a darkened place.
3. PET bottles will allow the beer to go flat over time. PET "breathes" in a sense, so the carbon-dioxide can escape. I'm not certain if a similar exchange of oxygen can occur. IF so, this would risk the beer becoming oxidized. PET bottled beer should therefore be consumed within a few months of bottling, which doesn't allow you to take the time to age your brew properly. And yes, aging beer does allow flavors to develop and some of the harsher flavors to mellow, particularly in darker beer recipes.
4. Sanitizer will not clean a scratched PET bottle properly at all. If you've needed to get a brush into the bottle, chances are it will be scratched, and therefore more difficult to keep clean for your next brew.
5. Scratches both inside and out can weaken the bottle so that even a mildly excessive pressure can allow the bottle to rupture.

Your best bet is to keep your brews in either bottles or kegs. In my experience, kegs will allow beer to age better than in bottles, and your bottling time is reduced to filling a keg or two in a few minutes, rather than spending ages adding extra sugar and filling 30+ bottles. Maintaining kegs is somewhat easier than maintaining bottles, but the initial setup is more expensive, and it can be fiddly getting your beer cold without modifying a fridge, or spending even more cash on a specialized fridge. Glass bottles is therefore the more cost effective compromise. Most home brew shops will be able to sell you a crate of bottles, or if you have a favorite brew, just save the bottles for your next brew. Larger glass soft drink bottles can also be used if you can find them, but the caps need to be replaced from time to time as they lose their ability to maintain a seal after a while.

Coopers does a range of very cost effective PET bottles in brown (http://secure.coopers.com.au/shop-diy/bottles-caps/). I've had good results using these and various soda bottles including cola bottles. To avoid light getting in I place the bottles in a cardboard box which would also regulate the temp a bit better and catch any mess if a bottle pops.

Not sure if this is a great idea but I also squeeze the bottles to get all the air out before putting the cap on. This refills with gas from the bottle fermentation. Doesn't seem to harm either way though.

I would avoid using bottles over 1 litre though as your second and third glasses from these bottles tend to cloud up as sediment is bubbled up from the bottle bottom as the pressure is released. A trick I use to avoid this is to decant into a pitcher.

These bottles are fine to use, just as long as you keep them in a dark place. They're generally even considered stronger than glass bottles.

If you're using a two liter, keep in mind the extra oxygen in the bottle if it's not full, it could make things taste a bit papery. You'll also end up with more yeast sediment at the bottom, so pour carefully if you don't like yeast in your beer.

Soda bottles are made of PET plastic, which is actually the same stuff that the "Better Bottle" carboys are made out of. The plastic itself is very compatible with beer. The biggest down sides are the color and transparency that others mentioned for light destroying the flavor.

The other area of concern is the caps and pressure. As far as pressure is concerned, these are designed for much higher pressures than beer. Soda is often closer to 30psi (beer's often served at half of that) and the bottles can handle something like 120psi before actually giving out.

The caps are designed for the same pressures. I would want to see if re-using the caps would cause oxygen leaks, but since the "new" caps just screw on too, I don't think that's a concern worth worrying about.

For me, I'd put the same beer into half a dozen PET bottles and half a dozen glass bottles. Then, at a month, 2 months, 3 months, 6 months, a year, etc. open a matching pair and taste to see how they compare. The best way to do this is have someone else pour them into glasses for you, so it's blind. If you can't taste the difference, go with the cheaper bottles. If you can, decide accordingly.