Republican: Limited government intervention.
Democratic: Big government.
That's definitely the most fundamental difference, and so many issues go back to that. Republicans: fewer taxes (INCOME taxes, I should say), less regulation of companies and, well, everything. Democrats: social intervention (like welfare), and other government interventions (like, oh I don't know...bailouts). Seriously, most of these things boil down to big or small government.
Oh, and Republicans believe in more of state's rights, while Democrats turn to the federal government.
My happy medium would be the Libertarian Party.