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In default Freeciv rules there are, despite anarchy, five forms of government. Despotism (initial government), Monarchy (a good transitional government from Despotism to future governments like Democracy and Communism, and is really good to make the cities grow, making the nation to expand), Democracy (great in peace time, but almost useless in AI games) and Communism (great for war) have well define roles, but Republic? It seems a pre-democracy, that may change anytime to communism. It is in expansionist nations almost unsustainable (I think) and unpredictable because it may fall to anarchy at any time.

I may misunderstood the republic government but is it role really important in any Freeciv strategy. I use it normally to make a linear change of government, but I don't know if I really need it.

I usually skip Republic too. Actuall, I can't recall ever using it. I'm always switching to Monarchy quickly, and then either Democracy (if I don't have to fear war) or communism (if I'm at war), though I often stay at monarchy during war because researching communism reduces the effect of cathedrals.
But Republic... Completely unused.

Sarilho1 wrote:it may fall to anarchy at any time.

No, it doesn't. It's more stable than Democracy in that there's no risk of failling to anarchy, and military units cause less unhappiness (I think a lot depends on whether you play with 'happyborders' or not - if units moving inside your own empire are not causing any unhappiness even in Democracy, that's not such a big difference). That said, in our games for the two last years Democracy has never been used without aggressive enemies immediately taking opportunity to conquer nation more restricted in military maneuvering. Republics still have a chance to defend themselves, while giving much higher income -> science output, than more military forms of government.

As cazfi said, Republic is more productive than Monarchy. Cities in a Republic get much more trade. Also, a Republic grows larger before unhappiness becomes an issue. Finally, a celebrating city in Republic can grow every turn. Personally, i skip over Monarchy and research Republic right away.

I've never had problems fighting the AIs with Democracy. Yeah, happyborders usually on. But also Shakespeare's Theatre for the city producing naval units, so they don't cause unhappiness. J. S. Bach's Cathedral. Decent luxury rate. Have strongly defended cities and concentrate your expeditionary force on a single city at a time. Or use diplomats in cease-fire/peace modes to take cities, ignore the AIs in wartime, and go for spaceship victory.

Borders + big cities is an offensive tactic by itself, as you suffocate nearby foreign cities.