What are some good tactics for the early game in Risk?
If you are an offensive player, Craig Reade wrote a good strategy page discussing starting in South America, which is a continent I like to start in, if I can.  The basic elements of the strategy are:


Don't play defensively.  You'll get boxed in and die.
You don't want to gain the continent, but lose the game because it cost you too much to take it.  That said, if you are not holding onto the entire continent early, you'll find yourself in an indefensible position, surrounded by foes and your turns will be numbered.
Grab some North American territories during initial placement - especially Central America.  North America is likely to be the next area you'll be heading into, so any territories you can grab now, go for it.  Plus Central America makes a great early buffer against attack.
Don't play defensively.
Ideally, plan on having gained a second continent before your Australian opponent starts their offensive push.
Don't allow yourself to get trapped.


If you can hold both of the Americas, you're in excellent position: 2 continents with 13 territories and only 3 access points.  Sweet.

Not sure if I mentioned this, but you don't want to play defensively ;-)