Thats a good question. Just for clarity sake I'll assume you mean a republic, and not pure democracy since that would essentially be mob rule.
I think people take it for granted that its the best system because the countries that use it are currently the most prosperous in the world. There are some things that go hand-in-hand with our current flavor of democracy though, like capitalism, good checks and balances, having 2 or more political parties, etc. Take those tweaks away and I'm not sure democracy has that much of an edge over other systems. Look at how China is developing as an example, the key piece of success in that country was free markets, not democracy. You could have a democratic communist system, but my gut would be that it would fail.
Looking at democracy, it has a bunch of weaknesses:
1) It can ostracize the minority
2) It's policies tend to change like fashion
3) Uninformed and/or uneducated voters elect bad leaders
4) Politicians are generally corrupt
5) Politicians are disincented to provide visionary leadership
6) Its always in the politicians best interest to appease the masses, and defer problems until after their term. See the patriot act, social security, Medicare as great examples.
But for all its failings, it has some plusses that don't exist in other systems:
1) A routine way to get rid of problem leaders (elections, impeachment)
2) People are less likely to riot when they have a say, even if they're the minority viewpoint. The empowerment provides hope.
3) A means of prioritizing and addressing the concerns of the majority of the country
I guess to summarize I don't know the answer to your question. I don't think our style of democracy is perfect, and there are improvements that could be made if we had the chance to start over. But I think our system works well enough as it is to keep the majority of people happy enough to endure. I wouldn't want to risk radically changing it, since thats a feat not too many governments have pulled off long term throughout history. The risk of picking a worse system is high.