If you hate rolling dice, here's a handy alternative: A Million Random Digits with 100,000 Normal Deviates by, appropriately enough, the RAND Corporation. While I think the concept of a book of random numbers is a bit dated, the reviews of the book at Amazon are a good read. And if you click "Surprise Me!" on Amazon's "Look Inside" menu, it says "This is a random page from a small sample." Well, duh. Of course it's a random page.
It turns out that generating good random numbers is hard, unless you really want to roll lots of dice. People do a terrible job of faking randomness. Even if you have reasonably good random numbers, using them properly is also hard. Most computer games depend on computer-generated random numbers, but I would never play one that involved real money online. Read this if you can't imagine why not.
If you need to make a decision, check out the coin flipper on random.org.