The biggest reason that Hitler was able to be elected was indeed his personal charms. He was able to build on the fears of the German people and promise them that he could make changes that would improve their lives.
It should not be hard for us in America to imagine how a charismatic man who promises change was elected. And, yet, people now do not like many of the changes such as in health care, etc. Yes, Hitler used the word "change" as well, cloaking much of his plans in rhetoric. As post #2 states, the economic problems of Germany were dire; the people knew who the merchants and storekeepers, and lawyers, and doctors were. So, they easily saw these non-Germans as the reason for their economic distress.
You have to remember here that these people did not know what we know now. It's not like Hitler came to power promising to kill all the Jews in Germany and then to expand out and get more Jews and kill them too. Sure, he was clearly anti-Semitic, but that was not that uncommon in that time and place and there's a huge gulf between voting for an anti-Semite and approving of the Holocaust.
Think of this analogy. Many Americans don't like illegal immigrants and would vote for people who speak out in favor of taking rights away from illegals, right? If one of those people came to power and started actually killing the illegals, would that mean that we had voted to kill illegals? I think the same applies to the case of Germans and Hitler.
Historical context and personality are two major reasons. Adolf Hitler rose in popularity and power during the 1920s and early 1930s, turbulent and depressing times for most Germans as they lost their empire, their national pride, and their personal dignity. No surprise that a nationalist who was a natural speaker could motivate the masses to believe in him. He promised them work, he promised them a return to glory, he promised them he would ignore the Treaty of Versailles and that he would punish those he scapegoated as responsible for Germany's misery, the Jews and the Communists.
When the worldwide economic Depression took hold by 1932, Germans were ready, tired, and a little desperate, so millions of them voted for Hitler's National Socialist Party (he himself was never elected, but appointed).
Check out Child of Hitler by Alfons Heck, and you can get some idea of what Hitler's appeal was to ordinary Germans.