Two German players, Horatius Caro and Marcus Kann, introduced this defense into competitive practice during the second half of the nineteenth century. Romantic gambits were popular among players of the time, so it's hardly surprising that this defence was regarded as being dry and boring. Its popularity only began to grow after the discovery and general acceptance of the basic positional principles. Early in this century, several masters recognized the advantages that it offered, and even a world champion, in the person of Capablanca, had it in his armoury. The great Cuban is acknowledged to have been an outstanding positional player, and later adherents of the defense were to be competitors of similiar inclination (Flohr, Botvinnik, Smyslow, Petrosian, Karpov, etc.).
Black's first move (1 ... c6 in reponse to 1 e4) is aimed at obtaining a foothold in the centre by way of d7-d5. The concept is strongly reminiscent of the French defence, but the development of Black's queen bishop is, as a rule, smoother. Admittedly, it does have the inherent disadvantage, as compared to the French, that after 2 d4 d5 3 Nc3 (3 Nd2) Black, in the absence of any other useful move, has to part with his centre pawn by 3 ... dxe4 -- thus relaxing tension in the centre.
The middle games which develop from the Caro-Kann are generally sound and of a rather positional character. Direct attacks against the king are rare in the early stages of the game. Flexibility is one of the chief advantages; Black remains uncommitted to any particular pawn structure. None of his pieces have any sort of development difficulty that might influence the whole opening (remember the problems that the queen's bishop has in the Queen's gambit declined.) The Caro-Kann defense is clear, relatively easy to learn, and therefore an eminently practical system. You can usually find your bearings without being completely familiar with the theory. Only a few particularly sharp variations require theoretical knowledge. The fact that Black is able to avoid the pitfalls of the dangerous gambits was evidently considered to be one of the Caro-Kann's advantages in the last century.
However, the disadvantages should not be swept under the carpet. The initiative rests principally with White, while in a number of variations Black can only achieve equality in positions of a simplified and drawn character. Yet it must also be said that the game does not proceed inexorably towards a quick draw, the reason being that the pawn structures are asymmetrical and there is no mutually open file that would lend itself to the early exchange of major pieces.
White frequently acquires a space advantage, due mostly to the absence of the centre pawn. Luckily, this is a type of advantage which is most difficult to capitalize on. Moreover, the danger of White overextending himself and throwing caution to the winds is always present.
Which variation should White choose?
I do not know which of the alternatives is the most dangerous. The choice also depends a lot on fashion. One master may prefer one particular variation, another a different one. Lesser players tend to follow suit. The variation 2 Nc3 and 3 Nf3 was very popular for twenty years, but is practically an extinct species in today's competition practice. The situation is much the same regarding the closed variation (3 e5). 2 d3, on the other hand, is a move which not so long ago was hardly ever contemplated, and then only by reckless eccentrics. Nowadays it presents serious problems to those using the Caro-Kann.
The Panov variation, which resembles the Queen's gambit, has for decades been the critical test of the Caro-Kann defense. This is the sharpest of the variations, and the complications arising frequently surpass those of the King's gambit.
Instead, the natural continuation 2 d4 d5 3 Nc3 has proven its worth and has been popular right up to the present day. After 3 ... dxe4 4 Nxe4 the continuations 4 ... Bf5, or 4 ... Nd7 and 4 ... Nf6 are equally popular
Finally, it should be added that the continuation 2 d4 d5 3 exd5 cxd5 4 Bd3 has also had devotees at various times (Fischer!), though it has never been a main variation.