It, of course, depends entirely on the year.

In 1942, the "official" successor might well have been thought to be Herman Göring: Göring had been the more-or-less official "Number Two" Nazi ever since Hitler had Röhm killed back in 1934. But the problem with Göring is that he was an opiate-addicted buffoon by this point, and increasingly marginalized by the other top Nazis. Muscled out of the economic ministry (which he had horribly mismanaged), Göring was made head of the Luftwaffe because it was a safe place to "park" him--a place where he would do the least damage, and have the least power. And Göring didn't even take that role seriously, instead spending a lot of time hunting, collecting art, designing new uniforms for himself, eating robustly, and getting high on morphine.

The single most powerful (and terrifying) man in the Third Reich by 1942 was, without question, Heinrich Himmler, who had absolute control over the SS empire. But Himmler's role as head of the SS actually served to isolate him from the Nazi Party to no small degree... it was a full-time job to run the SS, and Himmler was a micromanager. And the SS was an organization apart from the Party. Many Nazi Gauleiter (district leaders) hated Himmler, and felt trampled on by him and his almighty-SS. Himmler would have been unlikely to receive support to replace Hitler. Himmler was also perhaps too much of a bland organizer/manager than a "leader" in the Nazi vein... no less brutal, but a lot more bureaucratic.

Reinhard Heydrich was definitely being groomed to replace Himmler--and perhaps even Hitler, in a post-war world. Handsome, charismatic, courageous, intelligent, a cultured music-lover, and a die-hard racist, Heydrich was the epitome of any idealization of what a "Nazi" (and SS man) was supposed to be. Too bad he was killed by the Czech resistance in '42. (too bad for him, anyway--not for us :-)

Goebbels was never really in the running, despite his powerful role as propaganda minister. Or maybe because of it.... because when Goebbels was originally appointed Minster of Propaganda in 1933, he was furious--thinking, probably correctly, that the post was a way to sideline him. Many of the other top Nazis never trusted him--they thought he was too intellectual (!), and perhaps a bit too familiar with the 'socialist' wing of National Socialism. (note: he was still a right-winger... just more of a populist.)

BlueDahlia77 wrote that the successor might have been Hess, but no way... not by 1941. In 1935, Hess was to Hitler as Heyrich was to Himmler in '41... that is, a sort of bright-eyed successor-protege, and Hess was, indeed, officially the "Deputy to the Führer." But by 1940s, Hess' star had plummeted. Indeed, Hess' "mission" to the UK in 1941 was a fools mission--the depressive Hess was despondent at no longer having Hitler's attention (and at being excluded from Hitler's inner circle), and so was trying a desperate gamble to "bring the Führer peace with England" (before the invasion of the USSR). Hess only ended up a profound embarrassment.

In a power-struggle after 1942, though, the probable successor to Hitler would have been the least well-known of the top Nazis: Martin Bormann.

Bormann was the "Brown Eminence" (Fest)... the power-behind-the-throne, man-behind-the-scenes of the Nazi party and Nazi state. Officially the "Secretary to the Führer," Bormann was a master-intriguer, a cold calculator, constantly scheming to undermine Himmler, Göring, and even Goebbels. When Hess made his disastrous flight to Scotland (and to captivity), Bormann subtly took over the role (but not the title) of Deputy to the Führer. Bormann thereafter controlled access to the Führer... and insinuated himself into every nook and cranny of the Nazi Party. In any power struggle among top Nazis, I feel pretty sure Bormann would have ended up on top.

The best book about the 'inner circle' is still Joachim Fest's The Face of the Third Reich, with witty (and occasionally sharp) writing... even though the section on Hitler is outdated.