Yes you can inject it, and it will get you drunk much quicker. It is very bad for you. But not necessarily any worse than injecting any other drug. Why don't people do it? Well, cause its a lot easier to drink it.
I have heard of people who, because of years of drinking, have done extensive damage to their mouth, throat, and stomach and are no longer able to absorb alcohol efficiently from their stomach. So they do what steve100 was talking about and give themselves alcohol enemas. It wouldn't surprise me if some of them also use Intravenous methods to get their fix. I think the biggest problem with it would be getting the needles. The other problem with it would be being able to give yourself a shot while you are drunk or detoxing. It would be far too difficult.
Lastly, it would be much more dangerous. When alcohol is drank, your body is able to metabolize some of it before it has any effect on you. That is why just one shot or a few sips don't get you drunk. However, injecting it directly into the bloodstream would bypass this effect and make all of it absorbable, thus making it much easier to OD.