Ah yes, the classic game; the version most of us are introduced to, when continents were peanuts compared to how insane card sets could get. This version of the game can pretty much be explained entirely in terms of how risk cards are related to every aspect of gameplay. In fact, that's exactly what I'm going to do.
Before I explain anything else, perhaps I should explain exactly why Risk cards are so important in this version. In the beginning they seem relatively harmless, starting at only 4 armies for the first set. But this quickly snowballs to 15 by the 6th set, and by the 9th set you're already pulling 30 for a set. Additionally, if you own the territory printed on one of the cards you turn in, you get an additional two armies to sit on that territory; a wise player will recognize that securing their card territories is an absolute priority for building a mega-stack of units for later in the game.
This is, in fact, why the logic of the game can seem a bit backwards at times: to a new player, it seems like one should just conquer one territory per turn, since you never get more than one card even if you conquer half the board. They fail to recognize the logic of pushing for the card territories, that sometimes some initial over-expansion is necessary to acquire the armies needed to achieve your short term goals.
Conventional wisdom among casual players would suggest that continents are most critical at the beginning of the game, and totally lose their relevance by the time the Risk sets are increasing by fives. This couldn't be farther from the truth: in the beginning your focus should be on getting your position to correspond with your initial card territories. Each card territory, up to 3 per set, gives you an extra option as to where to place your stack, and thus which continent to try going after. At the very least, each card territory represents a stack of three units in the middle of nowhere, which is probably the most annoying for your opponents to deal with. The nice thing about these territories is that you can promptly abandon them since they won't offer that benefit ever again unless the game drags on long enough for the deck to be reshuffled; and if people are playing with any amount of brains in their head, this will never happen. You can instead head for whatever continent you consider to be the proverbial greener pastures.
Continents, ironically, don't begin showing their true value until Risk sets are getting high into the double digits. Since you can't possibly play a set every turn, you need the continent bonuses if you're to have any hope of competing during the brief periods where no sets are being played. If you're just stuck in a remote part of Asia scrabbling for Risk cards, the only thing in your future is for someone else to come after you with a card stack so they can eliminate you and acquire your precious cards. If you're sitting on four cards and a nearby player has two left after playing three, you've just handed him the victory: the rules force you to play a set if you ever have 6 or more cards, even if it's mid-turn. Players with continents, on the other hand, still have the ability to harvest cards and gather enough armies to defend their borders, and are less likely to be eliminated first.
As stated, a player who can be eliminated is a boon and a liability. If his conqueror triggers a forced card trade-in, it's that many more armies with which he can try eliminating yet another player. This can potentially keep firing off until he wins the game. This can be hard to avoid if you have four cards (the most you can have and still not have a set) and are stuck somewhere in Asia as in the aforementioned example: you don't have any armies to speak of, and one bad role can weaken you and still leave you with no cards to play.
It should come as no surprise that diplomacy in this game, when done correctly, is going to focus on achieving these steps. Everyone wants to secure a home area with their first card set, everyone wants a continent, and no one wants to be the guy stuck in Asia who can be eliminated at anyone's pleasure.
Let's talk about the continents a bit. It's usually safe to say that Asia will always be a no-man's-land in any session: too hard to secure with too small a benefit. The only way to secure Asia is to also take Australia and the European territory of Russia, limiting you to 3 borders; but by the time you managed this, you'd either be winning the game already or someone else would have the Risk cards necessary to render all that work moot. Africa and Europe are natural enemies, as both need to secure the Middle East, and their long frontier means that destroying the other is a necessity for survival. The Americas are one of the more broken aspects of this game: The one that unites first can easily conquer the other, and once you control both you have the same value as Asia with only three borders. We'll talk more about the strategic value of continents in the 2008 edition.