Absolutely. Despite what 3D says Jackson was an extremely significant president. Though reviled by those who don't appreciate Jackson's populism or his attitude towards a national banking system and his policies towards Native Americans would make him a war criminal by todays standards (but that's true of most of the U.S. Presidents who proceeded him).
Some of Jackson's most important accomplishments was that he was really the first modern U.S. President. He believed that the President represented all the people and was more than just an executive. He expanded Presidential powers, creating a stronger and more effective central government, he also was quite effective at eliminating corruption and limiting the power of machine politics at the national level. He was also the first U.S. President to pay off the government debt and balance the budget.
Jackson's most important contribution to Democracy in America was his response to the Nullification crisis. Jackson basically introduced a Bill into Congress that would have authorized him to use troops to force the State of South Carolina, or any State attempting to nullify federal law or seceding, to submit to the law. It was Jackson's most important contribution to the Republican form of Democracy as it established the precedent and law that States could not unilaterally nullify federal laws nor unilaterally secede from the Union. Amazingly, even though the principle of nullification was thoroughly rejected by U.S. legal jurisprudence almost 200 years ago there are those in the South who still argue it's validity and almost always make that argument when the courts have expanded the rights and liberties of some minority group. The fact that Jackson, the person responsible for discrediting nullification, was also a Southerner is also ironic.