Personality
Contrary to what Dr. McCoy might tell you, Spock does have a personality. It's distinct and multi-layered, and - like most of us - he'll act differently around different people. Very few get to see the "real" Spock under the Vulcan cool, and we might be just as grateful for this!
If you were to meet Spock just briefly, as many diplomats and other guests on the Enterprise do, you would note that he is polite, speaks economically, is fairly unexpressive, and is gentle towards children and small animals. The absence of emotional display is understood to be a Vulcan trait, not a sign of rudeness or disinterest. While he seldom smiles, he's usually in a good mood; it can be quite clear from his tone when he's not! Spock's sense of humour can be difficult to interpret, but Dr. McCoy knows when he's been teased, and Starfleet's higher ranks know when they've been insulted. Spock's affection for Kirk - on the other hand - is widely understood, and often displayed, if seldom subject to comment.
Yet underneath this facade of the well-functioning officer, Spock is constantly trying to keep his passions from overwhelming him. Certain phenomena encountered in space act as catalysts for his feelings. In The Naked Time, he breaks down in tears, lamenting how he could never express love for his family. In This Side of Paradise the spores cause him to give in to amorous feelings for the lovely Leila Kalomi. Biology brings out a violent streak in Amok Time, and time travel strips him of all inhibitions in All Our Yesterdays. Lust, rage, pain: all are part of Spock's make-up and inevitably boil to the surface.
As Spock develops throughout TOS and the film series, his disposition changes significantly. Before his death in The Wrath of Khan he is all Vulcan - or believes himself to be. He still has trouble with humour, and though he realizes the value of emotion in The Motion Picture, he hasn't incorporated its expression into his personality. When revived, he is trained to display his feelings when appropriate, has a wry, knowing wit, and accepts his human heritage.
What's appealing about Spock throughout his journeys is his combination of innocence and naiveté with dark, alien mysteries. And also, it's hard not to like someone so courteous. In using words like "shall" he is quaintly charming and shows he hasn't quite grasped contemporary Earth language. Like his friends Jim and Bones, he's always a little out of place on a 23rd century starship. Viewers have long sympathized with his sense of alienation. Both his positive characteristics and pent-up negative feelings are a draw to viewers, and contrast between them provides dramatic tension.
Whether raising his eyebrows and approaching a smile, straining and sobbing, giving routine readings, or yielding to violent passion, Spock is always captiviating, and his personality has endeared him to millions.