Here's why many people prefer Republic over Democracy. I, for the record, voted for republic back when this thread was new.
First off, there's nothing wrong with Democracy. It's a good government, as good as or marginally better than Republic in many respects, except for war weariness. Going back to the original poster's question, it's certainly a better government for peacetime than Monarchy if you're serious about keeping the peace (and Monarchy is certainly a better wartime government than Democracy if you're in for the long haul).
The problem with Democracy is that it is only marginally better than Republic. It has its bonuses, but in order to receive them, you have to undergo a second anarchy period (from Republic/Monarchy). Unless you are religious, you are potentially throwing away hundreds of gold and shields that your cities would have made under their current government down the toilet to get corruption that is slightly less than what you experience under Republic. It's like spending a few thousand dollars to put a new engine in your car that gets better fuel efficiency so that you can save $10 per month on gasoline. You would have to stay in Democracy for a long time to truly come out ahead by the numbers just in corruption.
For the 1.5x speed workers, they're great but again, by this time most of your highly productive cities should already have their tiles fully improved (if not, you aren't building enough workers!), and IIRC, unless your civ is also Industrious, it is only workers of your nationality that get the speed bonus, captured slaves work at the same speed as before due to truncations in the way the game calculates worker speed (I am not sure of this, it's been a while since I've tried). It IS very nice, though, for putting out those rails when you get to Steam Power.
Immunity to propaganda is a nice side bonus, but you won't find the AI attempting too much in the way of propaganda (though once in a while you'll find an AI who falls in love with spying and does it all the time to you). It's not enough to make or break this deal either way.
The trade bonus is probably the best part about Democracy, but it's exactly the same bonus that you get from Republic.
And finally, the War Weariness. If you've got most of the luxuries and lots of infrastructure and one or two of the big happiness wonders like Bach's and Sistine, then you can do a lot with warfare without invoking the weariness. If you're lacking these things and only have three or four luxuries and not every city has a cathedral and you didn't get Bach's and Sistine (pretty much the situation in the late Middle Ages on a typical Deity or Emperor game), you'll feel the pain if you try to wage war.
In short, if you're a Religious civ, it's a great government since you have very little to lose from making the switch.
Now, the benefits of Republic:
-Nearly as low of a corruption level as Democracy, much earlier in the game.
-Only requires one anarchy period. Like I said before this is a trivial point if you are religious but for everyone else this is a significant bonus.
-Same trade bonus as Democracy. This thing is the king of governments. Given the same civ with the same number of military units, you will make more cash with Republic than you will with Monarchy, even for very large numbers of military units (perhaps ESPECIALLY with very large numbers of military units, depending on how many cities you control).
-Extremely resistant to war weariness if the other civ is the aggressor. There are so many ways to get another civ to declare war on you that I won't bother listing them. The "other civ has to be the aggressor" stipulation shouldn't stop anybody from getting the war they want when they want to have it, and to pursue it much more thoroughly than they could under Democracy. Also, if the AI declares war on you of its own accord (i.e. you got sneak-attacked), you are given much freer reign to deal with it than you would under a Democracy (which must work to keep the fight limited or you'll be facing ANOTHER anarchy period to drop into Monarchy). If you're playing Chieftan-Regent and find yourself half an age or more ahead of the other civs with twice the number of units, than this isn't such an important point, but on Emperor, Deity, and to a lesser degree Monarch, it's possible to find yourself facing a larger, more advanced AI army that could conceivably do some serious harm to you if it were to get itself worked up over something.
In short, the reason why Republic is preferred over Democracy is not that it is markedly better, but that it's good enough to not warrant a change. It's that much better than Despotism (which penalizes your tiles and hogties you with forced labor rushing) that an anarchy period of any length is worth undergoing to reach Republic, but the benefits of undergoing a second, potentially long period of anarchy to go from Republic to Democracy are slim enough that it's usually not worth the switch.