1  You can make settlers build roads^ irrigation^ etc. in one turn (instead of the normal 2 - 12).
2  Make the settler unit build a road or irrigation.
3  When, in the same turn^ an other unit highlights^ go back to settler, and click on it.
4  Now the R or I disappear. Make the unit build a road or irrigation again.
5  Repeat this a few times until the desired advancement is build.

Extend movements (cheat)

Move ships long distances in one turn in pairs by passing a cargo unit back and forth. Move land units long distances by having them go on sentry duty in a city and reactivating them the same turn. Having ships 'steal' loads. A ship will load as many units as it can when it leaves a square^ including at sea when another ship just ended its turn at the same spot.

Make unit move twice each turn (cheat)

1  Move your units as usual.
2  Save the file.
3  Quit Civ and open this file.
4  Now you can move your units again^ while the year hasn't been changed. However the amount of money^ etc. hasn't been changed yet. This can be handy if barbarians arrived and you can't reach them with your army in one turn.

Cheap wonders and units (cheat)

In Civilization^ If you want to buy a wonder/unit/improvement (a rush job) the price per resource for improvements^ units and wonders is different. If you want to buy a wonder immediately for the cheapest prize^ do this:

1  Select the cheapest unit or improvement.
2  Buy it. This is quite expensive because the price doubles when your resource box is empty.
3  Now select the most expensive improvement and buy it. The price per resource for improvements is cheapest of the three. Next units is cheapest^ and the price per resource for wonders is the most expensive.
4  Now select the desired wonder^ and buy the remaining resources. This process can save up to 50% of the costs. That's a nice amount given the price of wonders.  

See the whole map in the small map window

1 Wait until your screen saver shows up. (This cheat seems to only work with After Dark or Disney AD screen savers!)
2 Move the mouse and see the whole map for a few seconds!

Get military on a forbidden square (cheat)

Use a diplomat or caravan to enter a square a military unit could otherwise not reach and then occupying it in the same turn with the military unit.