* Have a good feel for odds when you go into battle. Consultation of a risk odds calculator can be helpful. Here's one on the web:
http://bartell.org/cgi-bin/risk.cgi.
* Keep careful track of how many reinforcements each player will get, and how many cards they have. Keep an eye out for weak players with lots of cards, because everyone will want to take that player out. In games with 5 or 6 people, and escalating cards, you often see games that suddenly end when one player wipes out another, takes their cards, cashes them, and continues on with each subsequent player falling like dominoes.
* In an escalating game, try to be the last person to cash in cards (unless you REALLY need them earlier). In a flat game, try to hold out for red-blue-green cards if possible; also in flat games, it's often (though not always) a benefit to be the first to cash them in, to make the first big expansion.
* In cards games, try to grab a card every turn. It can be useful to make an alliance where you agree to leave a bordering country with only 1 man in it, and then each of you take turns attacking the country, getting a card with minimal danger. In No-Cards game, realize there is a diminished benefit in attacking another country every turn. Try to build up strength instead, if possible.
* If possible, try to grab a continent out of the way and unthreatened at the start. Avoid continents in the middle, between two opponents. Continents with the least number of access points are also good. North America is worth the same as Europe, but Europe has 5 access points (or maybe 6 depending on how you count),whereas NA only has 3. Keep the smallest border possible (if you have Europe, you should try to hold North Africa if at all possible, because of its two entries into Europe. The Middle East is also a key.
* Don't forget that the bonus you get for every 3 countries you hold above 9. In some of the big maps, you can get a huge bonus from being spread out widely. In some of the big maps, it can be a great alternative to owning a continent, because people don't view you as much of a threat.
* Avoid making other players think you're the biggest threat until you can fend off all attacks. Taking a big continent too soon should be avoided, except perhaps in 3-man games with unlimited fortifications, since you can shore up the defenses.
* Make alliances if possible, or at least try to focus attention on another player. Offering to make one border a DMZ is often appreciated early in the game. Later on, cooperation to stop a juggernaut can be possible, if you're in a weak position. Suggest that other players have grown too strong. And if possible, let other players do your work for you in taking down a dangerously strong opponent.
* If you make an alliance, set a limit on how long it'll last (for instance, to round 4), or a condition for it ending (examples: when one or the other's turnwise reinforcements are greater than 6, when one or two other players have been wiped out, or when any of the allies has more than one continent). Never be the first to break it. You can also generate good will by promising not to attack a certain player, without asking anything in return.