Absolutely - switching governments is key to doing well.
In despotism and anarchy - the two worst govs - you lose one food, one gold and one shield for any tile which has three or more. So a mined hill is three shield in e.g. republic, but only two in despotism. That, alone, is reason enough to swap as soon as you can.
Despotism also has crippling corruption, so cities far from your capital are nearly worthless, with likely only one shield and one gold per turn, which hardly contributes to the civ, and may actually make a loss.
Monarchy is a good warmongering govt (Domination and Conquest victories) especially for less experienced players, since there is a lot of free unit support, your people never become war-weary and you can use military units in your cities to keep people from being unhappy.
Communist is like that too, except it's better for widely spread empires (where the corruption spreads evenly, so all towns contribute a little) but your core is more corrupt than monarchy. You get more military police to keep the cities happy, and can use population to rush projects, just like in despotism.
Democracy is the peaceful route to victory. You get extra-fast workers, bonus gold in almost all tiles, very low corruption. Downside is your people don't like war and you pay for all your units. Diplomacy or Space Race are good for this.
The all-round best IMHO is Republic. You get most of the pluses of democracy, with a bit more corruption and a bit more resilience to war weariness. Once you get to understand how to manage the happiness of your people with luxuries and entertainment tax, you can wage almost continuous war as a Republic.
Tips for switching:
Religious civs take only a one turn anarchy when switching, so can switch at will. Long war - go commie or monarch. Peace - go back to republic or demo.
Non religious need to be more careful. If you know you're going to war a lot, it might be worth staying in Monarchy, and may never be worth being a democracy. You'll lose more production if you switch a lot than you gain in the good turns. That's why Republic is so nice. It's a decent compromise and saves on the anarchies a lot.