I know there are already quite a few great bottle cutting instructables but I find this technique to be the fastest, and in my expirience the cleanest and easiest way to cut bottles. My project was to make a set of drinking glasses from old pepsi bottles that I had lying around, but you can use this technique for whatever project you like.
Step 1: Tools
All you really need for this is a simple glass cutter you pick up from a hardware store and a propane torch with a relatively fine tip. It may work with something else like a lighter, candle, larger torch etc. but I have yet to try those as my little benzomatic pencil torch has worked so well. My preferred way to do this also involves a lathe with a very slow speed but it can be avoided as I show later in the instructable. All you really need is some way to rotate a bottle at a relatively slow controlled speed, Ive done this on a potters wheel also but you could easily rig something up with a geared motor from a toy car, its only needs low torque.
Step 2: Nick
This is what makes this method so much easier, you dont need some jig to cut around the edge of a bottle perfectly all you need is a to make a little (like 1/8") nick with the glass cutter that would follow around the circumference of the bottle. It should be a decent nick with quite a bit of pressure applied to the cutter.
Step 3: Spin it (lathe method)
All you need to do now is find a way to rotate the bottle slowly, the way I like to do it is use my sherline lathe and set the variable speed to very low, I put a pencil in the tail stock so everything doesnt just fall down when the bottle breaks. Then you simply light your torch and hold in place over the nick while the bottle spins, after about a minute depending on the thickness of the glass there be a cracking noise and a line will appear all the way along the bottle. The bottle sometimes but wont always split in half, sometimes you just have snap it with your hands, be careful the edges will be sharp. As always be carefully the is fire, a spinning lathe, and the potential for broken glass. At the end of my video you hear a clicking noise its not from the glass breaking its because my chuck loosened and the bottle was falling between jaws, I would recommend wrapping a rubber band around the base of your bottle so you can get a better grip.
The crack is usually perfectly clean only requiring light sanding to smooth out sharp corners but sometimes you might get a slight bump the needs a bit more sanding, I usually just do another bottle because its so easy.
Step 4: Spin it (string method)
This is just one way to do this without a lathe, there are much easier/safer ways but this should give you an idea. You need something that will fit over the top or bottom of your bottle that you can attach string to. You could always just duct tape string directly to you bottle but this is more repeatable. I found that a water bottle cap was a good fit so I punched a hole in the bottom and tied some thin string to a piece of wood and taped that inside the cap. I then taped the cap to bottle and tied the string to my ceiling. Then I simply spun the bottle up to build up rotation in the string, I regulated the speed by taping it with my finger. Make sure you have something directly below the bottle so it doesnt fall too far and break.
Step 5: Enjoy
Do whatever you want with some cleanly cut bottles, I sanded my rims and made a nice set of pretty neat looking drinking glasses, the painted on graphics on the pepsi bottle looks cool and lasts well.