The second Broccoli produced James Bond film, 1963's From Russia With Love, is my personal favorite. It was made just prior to Goldfinger which was the film that established the formula to be followed in all subsequent films.

FRWL is very much an espionage thriller unlike most Bond adventures. The plot revolves around a Russian coding machine that 'M' instructs Bond to recover. The gadgets and scenarios exist in the realm of believability and contrast heavily with other Bond pictures. It's almost like a Hitchcock film in its plotting, and contains one of the best fight sequences in cinema history (Bond's duel with Donovan 'Red' Grant aboard the Orient Express).

I enjoy all of Connery's entries in the series (discounting Diamonds Are Forever) but find this particular one outstanding.