You can drill glass without breaking it, but you need to use the right tools. The first critical choice is what drill and drill bits to use. To cut glass, you'll have to use a drill bit made of either tungsten carbide or diamond. If you use a diamond drill bit, don't use a hammer drill, as that will damage the diamond drill bit.
When you decide where to drill on the glass, stay away from the edges and corners. You'll want to be at least three-quarters of an inch away from any edge to lessen the chance of cracking the entire sheet. Next you'll want to secure the glass; how you do this will depend on the shape of the glass. For example, you'll secure a glass sheet differently than a glass bottle. The key is to use something sturdy, yet soft, that can absorb the vibration. A rubber pad would work well under a glass sheet.
Once you start drilling, start with a slow speed and light pressure. If you're using a diamond drill bit, you'll want to start with a smaller size than you'll need later. Drilling can produce heat, so make sure to keep the area cool. You can use water by spraying the area or even placing the object in water as you drill it. A common recommendation is to drill just half way through the glass without breaking through it. Then turn the glass over and drill fresh from the other side. This can create a hole that's a bit off-center, but it reduces the chances of cracking the glass.
Lastly, remember some key safety precautions. Wear safety goggles, protective gloves and a mask (you don't want to inhale glass dust). Make sure the drill bit is securely fastened into the drill before turning it on.