Holding Continents
The game of "Risk" can turn on one player's ability to seize and hold continents. Controlling an entire continent grants you extra armies each turn, as well as a viable power base with which to launch offensives. Of the six continents on the board, Australia and South America are the most easily defended. Australia has only one point of entry, while South America has two. Europe and Asia, on the other hand, are difficult to conquer and even more difficult to hold. Consider holding off on them in the early parts of the game, and focus on holding one of the smaller ones if you can.
Watch Your Opponents
In "Risk," it can be easy to focus too much on what you're doing and ignore your opponents' actions. When formulating your plans, consider the other players in territories near you and what they may be capable of in future turns. It may be advantageous to thwart your enemy--for example, by seizing and holding a portion of a continent that he might otherwise control--even if it doesn't grant you any immediate benefit.
You may also wish to size up your opponents from a mental standpoint; someone who acts uncertainly or appears overly deferential is more apt to defend, while someone who does a lot of trash talking or bullying is more apt to attack. The more you know about the other players, the more readily you can predict their actions.
Flexibility
The conditions of "Risk" change all the time, and something that makes perfect sense one turn may be completely untenable the next. A winning "Risk" player learns to shift his strategy and deal with the way the board looks now rather than how it looked a few turns ago. This is especially pertinent with alliances and diplomacy, which aren't mentioned in the rules but are a key part of the game nonetheless. Alliances against a common foe, for example, cease to have meaning the minute that foe is defeated, and there's nothing that says you can't turn on a partner as soon as his usefulness ends. Keep your options open and prepare for a number of different developments; it will help keep you in the game.