Goldfinger, On Her Majesty's Secret Service, The Living Daylights, Goldeneye, Casino Royale.
I tried to keep it to one for each Bond (minus Moore, usually agreed to be the weakest Bond with the weakest films.) While I personally prefer From Russia With Love to Goldfinger, the latter is more action oriented and iconic, and probably a better film to get someone hooked with. The Living Daylights and License to Kill are both strong outings, but TLD is probably the better one to go with as it's more "classic Bond."
Those films should provide an excellent sampling for each Bond and are easily some of the high points of the series. After that it should be far easier to move on to some of the other films.