Short answer: Yes. I was smoking 25 full strength Marlboros a day until I picked up an electronic cigarette 15 weeks ago, and I haven't had one smoke since. I tapered off the nicotine over 6 weeks, and haven't had any nicotine for 9 weeks. I still use the e-cig in the evenings, so I'm not completely out of the woods yet, but I'd say 15 weeks without a fag is a success. I won't say it's been easy, but the one thing that made me stick with it was the thought that if necessary, I could always keep using ecigs as a relatively safe nicotine delivery system. I've gone quite a bit further than that, and while not easy, a lot easier than expected.
The only word of advice: get something decent, and not those stupid looks 'like a fag' things. I go the starter kit
here Well worth the money.