Risk (BGG entry), according to sources that prefer to call themselves voices and are not to be taken seriously, is one of the most successful, imitated and thus influential board games ever devised. It also is a particularly enjoyable game, that comes in a variety of flavours ranging from Star Wars to Lord Of The Rings to Classic, with the added bonus of being less prone to shatter friendships than Diplomacy. Also, also, Risk has the dubious honour of being the first truly mainstream wargame.
With wargaming, though, come tactics and strategies. Strategy guides too. Some of the best can apparently be found over at the rather specialized RISK, Strategies Explained… website. It even has a basic beginners guide. An advanced one too, obviously. Try them out in battle (for free), over at netRisk or by downloading the very Risk-esque Dominate Game.